A Banach space with an infinite dimensional reflexive quotient operator algebra $L(X)/SS(X)$

Abstract: I will discuss method of constructing a Banach space $X$ such that the algebra of bounded operators $L(X)$ is a direct sum of an infinite dimensional reflexive Banach space $V$ and the operator ideal of strictly singular operators $SS(X)$. The space $V$ is spanned by an unconditional basic sequence $(I_s)_{s=0}^\infty$ where $I_0$ is the identity on $X$, whereas each $I_s, s=1,2,...$ is a projection on some subspace $X_s$ of $X$. The multiplication on $V$ is defined naturally: $V$ is the unitization of the subalgebra of $L(X)$ spanned by $(I_s)_{s=1}^\infty$ with the pointwise multiplication.

functional analysis

Audience: researchers in the topic

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Banach spaces webinars

Series comments: Description: Research seminar on Banach spaces and related topics

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