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Closed injective ideals of multilinear operators, related measures and interpolation

Antonio Manzano, Pilar Rueda, Enrique A. Sánchez‐Pérez

Mathematische Nachrichten > 293 > 3 > 510 - 532

We introduce and discuss several ways of extending the inner measure arisen from the closed injective hull of an ideal of linear operators to the multilinear case. In particular, we consider new measures that allow to characterize the operators that belong to a closed injective ideal of multilinear operators as those having measure equal to zero. Some interpolation formulas for these measures, and...

article

Duhamel Algebras and Applications

M. T. Karaev

Functional Analysis and Its Applications > 2018 > 52 > 1 > 1-8

We introduce Duhamel algebras and study their properties and applications. We prove that a Banach space of analytic functions on the unit disc that satisfy certain conditions is a Duhamel algebra and describe its closed ideals. These results substantially generalize and improve the main results of Wigley’s papers. Some other related questions are also discussed.

article

Strong ideals and horizontal ideals in pseudo-BCH-algebras

Andrzej Walendziak

Annales Universitatis Paedagogicae Cracoviensis. Studia Mathematica > 2016 > 15

In this paper we define strong ideals and horizontal ideals in pseudo-BCH-algebras and investigate the properties and characterizations of them.

article

Gleason Parts and Closed Ideals in Douglas Algebras

Kei Ji Izuchi, Yuko Izuchi

Computational Methods and Function Theory > 2016 > 16 > 2 > 243-263

Recently, the study of the structure of closed ideals in $$H^{\infty }$$ H ∞ whose zero sets are contained in G, the union set of non-trivial Gleason parts, has progressed remarkably. We generalize these results to closed ideals in Douglas algebras A. For non-zero functions $$f_1,f_2,\ldots ,f_n$$ f 1 , f 2 , … , f n in A, $$I=\sum ^n_{j=1}f_j A$$ I = ∑ j = 1 ...

article

Ideals and atoms of BZ-algebras

Wiesław A. Dudek, Xiaohong Zhang, Yongquan Wang

Mathematica Slovaca > 2009 > 59 > 4 > 387-404

Ideals and atoms are studied by various authors from different point of views. In different algebras there are studied different ideals, but obtained results are similar. Below we present a new method of study of ideals in BZ-algebras. Using this method we describe the connection between ideals of various types.

article

Regularity of Segal algebras

G. S. Mustafaev

Functional Analysis and Its Applications > 2006 > 40 > 1 > 62-65

Let A be a Banach algebra. The second dual A** can be equipped with two multiplications, each of which is a natural extension of the original multiplication in A. The algebra A is said to be Arens regular if these two multiplications coincide. We give necessary (and, for some classes of algebras, sufficient) conditions for the regularity of a Segal algebra. We also obtain necessary and sufficient...

article

Closed ideals in C∞ with the Duhamel product as multiplication

M.T. Karaev

Journal of Mathematical Analysis and Applications > 2004 > 300 > 2 > 297-302

Let (C∞,⊛) denote the algebra of infinitely differentiable functions in [0,1] with Duhamel product (f⊛g)=ddx∫0xf(x−t)g(t)dt as multiplication. We describe all the closed ideals in (C∞,⊛). As a consequence we obtain that the integration operator I, (If)(x)=∫0xf(t)dt, is unicellular in the space C∞[0,1], which is the solution of a long-standing problem.

article

Closed Ideals of Holomorphic Functions with Two Generators

V. N. Khabibullin

Mathematical Notes > 2004 > 76 > 3-4 > 558-563

For a wide class of algebras P of holomorphic functions on a domain in ℂ, sufficient conditions are obtained under which a closed ideal I ⊂ P is 2-generated.

article

Prime spectra of non-commutative generalizations of MV-algebras

Ji Rachunek

Algebra universalis > 2002 > 48 > 2 > 151-169

Abstract. Non-commutative generalizations of MV-algebras were introduced by G. Georgescu and A. Iorgulesco as well as by the author; the generalizations are equivalent and are called GMV-algebras. We show that GMV-algebras can be considered as special cases of Grishin algebras. As MV-algebras are algebraic models of the ukasiewicz logic and Grishin algebras have the analogous role for the classical...

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Closed injective ideals of multilinear operators, related measures and interpolation

Duhamel Algebras and Applications

Strong ideals and horizontal ideals in pseudo-BCH-algebras

Gleason Parts and Closed Ideals in Douglas Algebras

Ideals and atoms of BZ-algebras

Regularity of Segal algebras

Closed ideals in C∞ with the Duhamel product as multiplication

Closed Ideals of Holomorphic Functions with Two Generators

Prime spectra of non-commutative generalizations of MV-algebras

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