Search results for: Grzegorz Lewicki

Items from 1 to 20 out of 35 results

article

DZIEDZICTWA I ZOMBIE. DLACZEGO NALEŻY WSPIERAĆ KRÓTKOTERMINOWE PROGNOZY ANALIZĄ ZJAWISK DŁUGOFALOWYCH

Greg Grzegorz Lewicki Greg Grzegorz Lewicki

PORÓWNANIA. Czasopismo poswiecone zagadnieniom komparatystyki literackiej... > 2019 > 24 > 1 > 269-273

Autor stwierdza, że praca TuckeramThe Legacies of Totalitarnianism jest niezmiernie ważna dla studiów nad postkomunizmem w Europie Środkowej i Wschodniej oraz dla historiozofii, która od czasów poheglowskich stroniła od holizmu. Zdaniem autora, Tucker trafnie identyfikuje ponadnarodowe składowe wspólnej tożsamości regionu, wynikające z tytułowych „dziedzictw” (procesów średnioterminowych wywodzących...

article

Sequence Lorentz Spaces and Their Geometric Structure

Maciej Ciesielski, Grzegorz Lewicki

The Journal of Geometric Analysis > 2019 > 29 > 3 > 1929-1952

This article is dedicated to geometric structure of the Lorentz and Marcinkiewicz spaces in case of the pure atomic measure. We study complete criteria for order continuity, the Fatou property, strict monotonicity, and strict convexity in the sequence Lorentz spaces $$\gamma _{p,w}.$$ γ p , w . Next, we present a full characterization of extreme points of the unit ball in the sequence...

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Best approximation properties in spaces of measurable functions

Maciej Ciesielski, Grzegorz Lewicki

Mathematische Nachrichten > 291 > 4 > 610 - 631

We research proximinality of μ‐sequentially compact sets and μ‐compact sets in measurable function spaces. Next we show a correspondence between the Kadec–Klee property for convergence in measure and μ‐compactness of the sets in Banach function spaces. Also the property S is investigated in Fréchet spaces and employed to provide the Kadec–Klee property for local convergence in measure. We discuss...

article

Uniform K-monotonicity and K-order continuity in symmetric spaces with application to approximation theory

Maciej Ciesielski, Grzegorz Lewicki

Journal of Mathematical Analysis and Applications > 2017 > 456 > 2 > 705-730

We investigate K-order continuity in a symmetric space E using the fundamental function ϕ of E. We also show a connection between reflexivity and K-order continuity in symmetric spaces. Next, we present several results devoted to a characterization of uniform K-monotonicity and decreasing (increasing) uniform K-monotonicity in symmetric spaces. We also discuss a relationship between decreasing (resp...

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A note on the admissibility of modular function spaces

Diana Caponetti, Grzegorz Lewicki

Journal of Mathematical Analysis and Applications > 2017 > 448 > 2 > 1331-1342

In this paper we prove the admissibility of modular function spaces Eρ considered and defined by Kozłowski in [17]. As an application we get that any compact and continuous mapping T:Eρ→Eρ has a fixed point. Moreover, we prove that the same holds true for any retract of Eρ.

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Bernstein’s Lethargy Theorem in Fréchet spaces

Asuman Güven Aksoy, Grzegorz Lewicki

Journal of Approximation Theory > 2016 > 209 > C > 58-77

In this paper we consider Bernstein’s Lethargy Theorem (BLT) in the context of Fréchet spaces. Let X be an infinite-dimensional Fréchet space and let V={Vn} be a nested sequence of subspaces of X such that Vn¯⊆Vn+1 for any n∈N. Let en be a decreasing sequence of positive numbers tending to 0. Under one additional but necessary condition on sup{dist(x,Vn)}, we prove that there exist x∈X and no∈N such...

book

Minimal Projections in Banach Spaces

Włodzimierz Odyniec, Grzegorz Lewicki

Lecture Notes in Mathematics

article

Asymptotic Behavior of Factorization and Projection Constants

Grzegorz Lewicki, Mieczysław Mastyło

The Journal of Geometric Analysis > 2017 > 27 > 1 > 335-365

This paper is concerned with estimates of important factorization constants that appear in Banach space theory. We prove upper bounds of the Hilbertian norm of projections on finite-dimensional spaces of interpolation spaces generated by certain abstract interpolation functors and show applications to Calderón–Lozanovskii spaces. We also prove estimates of the p-factorization norm and projection constants...

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Minimal projections onto hyperplanes in ℓpn

Grzegorz Lewicki, Lesław Skrzypek

Journal of Approximation Theory > 2016 > 202 > C > 42-63

The purpose of this paper is to find the relative projection constant of ker{1}={x:∑i=1nxi=0} in ℓpn for an arbitrary n (see Theorem 2.28). This extends a result of L. Skrzypek obtained for n=3,4. We also improve on the formula for the relative projection constant onto hyperplanes in Lp[0,1] obtained by C. Franchetti (see Theorem 2.21) and reprove a result of S. Rolewicz (see Corollary 2.11).

article

Subspaces of codimension two with large projection constants

Alberto Castejón, Grzegorz Lewicki

Journal of Mathematical Analysis and Applications > 2014 > 420 > 2 > 1391-1407

Let V be an n-dimensional real Banach space and let λ(V) denote its absolute projection constant. For any N∈N, N≥n defineλnN=sup⁡{λ(V):dim⁡(V)=n,V⊂l∞(N)}. The aim of this paper is to determine minimal projections with respect to l1-norm as well as with respect to l∞-norm for subspaces given by solutions of certain extremal problems. As an application we show that for any n,N∈N, N≥n there exists an...

article

Czas Jagiellonów bez zagonówCzas Jagiellonów bez zagonów

Grzegorz Lewicki

Res Publica Nowa > 2014 > 3 > 39-41

Even the army of innovative Poles will not help, if Poland cannot create new industries in the next twenty years. It is nice “The Economist” suggests Poland may be entering second Jagiellonian Age, but in fact we are more threatened by technological collapse. Thus we may be compared to Jagiellonians without fields, which were a key to Poland’s economic growth of the past. In a healthy society both...

article

Limit theorems for the numerical index

Asuman Güven Aksoy, Grzegorz Lewicki

Journal of Mathematical Analysis and Applications > 2013 > 398 > 1 > 296-302

We improve on a limit theorem (see Martin et al. (2011) [13], Th. 5.1) for numerical index n(⋅) for large classes of Banach spaces including vector valued ℓp-spaces and ℓp-sums of Banach spaces where 1≤p<∞. We introduce two conditions on a Banach space X, a local characterization condition (LCC) and a global characterization condition (GCC). We prove that if a norm on X satisfies the (LCC), then...

article

Uniqueness of minimal Fourier-type extensions in $$L_1$$ -spaces

Grzegorz Lewicki, Agnieszka Micek

Monatshefte für Mathematik > 2013 > 170 > 2 > 161-178

We give a characterization of uniqueness of finite rank Fourier-type minimal extensions in $$L_1$$ -norm. This generalizes the main result obtained by Lewicki (Proceedings of the Fifth International Conference on Function Spaces, Lecture Notes in Pure and Applied Mathematics, vol. 213, pp. 337–345, 1998) to the case of $$n$$ -circular sets in $$\mathbb{C }^n$$ .

article

Asymptotic estimate of absolute projection constants

Grzegorz Lewicki

Universitatis Iagellonicae Acta Mathematica > 2013 > 51

In this note we construct a sequence of real, k-dimensionalsymmetric spaces Y k satisfyingThis improves the lower boundobtained in [3], Th. 5.3 by maxw2[0;a2] h(w).

article

Asymptotic estimate of absolute projection constants

Grzegorz Lewicki

Universitatis Iagellonicae Acta Mathematica > 2013 > 51 > 51-60

In this note we construct a sequence of real, k-dimensional symmetric spaces $Y^k$ satisfying $ \text{lim} \ \underset{k}{ \text{inf} } \ \lambda_k^S // \sqrt{k} \ \geq \ \text{lim} \ \underset{k}{\text{inf}} \ \lambda(Y^k, l_1) // \sqrt{k} \ \gt \ \underset{w in [0,a_2]}{\text{max}} h(w) \ \gt \ 1//(2 - \sqrt{2//\pi})$, where $\lambda_k^S$ is defined by (4) and $h(w)=a_1^2\sqrt{2//\pi}+2a_1\sqrt{a_2^2-w^2}+w\sqrt{a_2^2...

article

Codimension-one minimal extensions onto Haar subspaces

Grzegorz Lewicki, Agnieszka Micek

Journal of Approximation Theory > 2012 > 164 > 11 > 1461-1471

Let Hn be an n-dimensional Haar subspace of CR[a,b] and Hn−1 be an n−1-dimensional Haar subspace of Hn. Let A be a linear, continuous operator on Hn−1. In this note we show that if a norm of minimal extension of A from Hn into Hn−1 is greater than the operator norm of A, then it is a strongly unique minimal extension. Moreover, we prove, with a slightly stronger assumptions, that minimal extension...

article

Minimal projections with respect to various norms

Asuman Aksoy, Grzegorz Lewicki

Studia Mathematica > 2012 > 210 > 1 > 1-16

A theorem of Rudin permits us to determine minimal projections not only with respect to the operator norm but with respect to various norms on operator ideals and with respect to numerical radius. We prove a general result about N-minimal projections where N is a convex and lower semicontinuous (with respect to the strong operator topology) function and give specific examples for the cases of norms...

article

Equality of two strongly unique minimal projection constants

Grzegorz Lewicki, Agnieszka Micek

Journal of Approximation Theory > 2010 > 162 > 12 > 2278-2289

Let P(X,Y) denote the set of all linear, continuous projections from a Banach space X onto a linear subspace Y. Let fˆ=(f1,…,fk)∈Rk be such that 0<f1⩽f2⩽⋯⩽fk, ∑i=1kfi=1. Define f(0)=(f1,f2,…,fk,0,…,0), f(j)=(0,…,0,1j+k,0,…,0) for j=1,2,…,n−k. Let Hˆ=kerfˆ and H=⋂j=0n−kkerf(j). In this paper we prove that the strongly unique minimal projection constant (SUP-constant) of the space P(l∞(k),Hˆ) is...

article

Minimal shape-preserving projections in tensor product spaces

Grzegorz Lewicki, Michael Prophet

Journal of Approximation Theory > 2010 > 162 > 5 > 931-951

Let X denote a (real) Banach space. If P:X→X is a linear operator and S⊂X such that PS⊂S then we say that S is invariant under P. In the case that P is a projection and S is a cone we say that P is a shape-preserving projection (relative to S) whenever P leaves S invariant. If we assume that cone S has a particular structure then, given a finite-dimensional subspace V⊂X, we can describe, in geometric...

article

A proof of the Grünbaum conjecture

Bruce Chalmers, Grzegorz Lewicki

Studia Mathematica > 2010 > 200 > 2 > 103-129

Let V be an n-dimensional real Banach space and let λ(V) denote its absolute projection constant. For any N ∈ N with N ≥ n define $λₙ^{N} = sup{λ(V): dim(V) = n,V ⊂ l^{(N)}_{∞}}$, λₙ = sup{λ(V): dim(V) = n}. A well-known Grünbaum conjecture [Trans. Amer. Math. Soc. 95 (1960)] says that λ₂ = 4/3. König and Tomczak-Jaegermann [J. Funct...

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INFONA - science communication portal

Search results for: Grzegorz Lewicki

DZIEDZICTWA I ZOMBIE. DLACZEGO NALEŻY WSPIERAĆ KRÓTKOTERMINOWE PROGNOZY ANALIZĄ ZJAWISK DŁUGOFALOWYCH

Sequence Lorentz Spaces and Their Geometric Structure

Best approximation properties in spaces of measurable functions

Uniform K-monotonicity and K-order continuity in symmetric spaces with application to approximation theory

A note on the admissibility of modular function spaces

Bernstein’s Lethargy Theorem in Fréchet spaces

Minimal Projections in Banach Spaces

Asymptotic Behavior of Factorization and Projection Constants

Minimal projections onto hyperplanes in ℓpn

Subspaces of codimension two with large projection constants

Czas Jagiellonów bez zagonówCzas Jagiellonów bez zagonów

Limit theorems for the numerical index

Uniqueness of minimal Fourier-type extensions in $$L_1$$ -spaces

Asymptotic estimate of absolute projection constants

Asymptotic estimate of absolute projection constants

Codimension-one minimal extensions onto Haar subspaces

Minimal projections with respect to various norms

Equality of two strongly unique minimal projection constants

Minimal shape-preserving projections in tensor product spaces

A proof of the Grünbaum conjecture

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