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In this paper our main goal is showing that many of quantization results in functional analysis are rather algebraic. Following Esslamzadeh and Taleghani (Linear Algebra Appl 438:1372–1392, 2013), we call every subspace [resp. self-adjoint unital subspace] of a unital $$*$$ ∗ -algebra, a quasi operator space [resp. quasi operator system]. Local operator systems can be realized as quasi...
In this paper we investigate algebraic structure of quasi operator spaces and quasi operator systems. We call a subspace of a unital complex ∗-algebra A [resp. self-adjoint subspace of A containing 1A] a quasi operator space [resp. quasi operator system]. Our keys in this investigation are the bounded subalgebra A0 of A, a C∗-seminorm on A0, and a new notion of algebraic bound.Our main goal is to...
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