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On Some Linear Operators Preserving Disjoint Support Property

Journal: Sahand Communications in Mathematical Analysis (Vol.18, No. 3)

Publication Date:

Authors : ; ;

Page : 41-49

Keywords : Disjoint support; Codomain; Linear preserver; Isometry;

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Abstract

The aim of this work is to characterize all bounded linear operators $T:lpirightarrowlpi$ which preserve disjoint support property. We show that the constant coefficients of all isometries on $lpi$ are in the class of such operators, where $2neq pin [1,infty )$ and $I$ is a non-empty set. We extend preserving disjoint support property to linear operators on $mathfrak{c}_{0}(I).$ At the end, we obtain some equivalent properties of isometries on Banach spaces.

Last modified: 2022-07-31 17:27:47