Property (gw) for tensor product and left-right multiplication operators

Enrico Boasso; B. P. Duggal

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arXiv · 1401.2031

Property (gw) for tensor product and left-right multiplication operators

Enrico Boasso·B. P. Duggal

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Abstract

Given Banach spaces $X$ and $Y$ and operators $A\in B(X)$ and $B\in B(Y)$, property $(gw)$ does not in general transfer from $A$ and $B$ to the tensor product operator $A\otimes B\in B(X\overline{\otimes} Y)$ or to the elementary operator defined by $A$ and $B$, $τ_{AB}=L_AR_B\in B(B(Y,X))$. In this article necessary and sufficient conditions ensuring that property $(gw)$ transfers from $A$ and $B$ to $A\otimes B$ and to $τ_{AB}$ will be given.

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BibTeX RIS

Enrico Boasso, B. P. Duggal. 2014-01-09. Property (gw) for tensor product and left-right multiplication operators. https://arxiv.org/abs/1401.2031

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