On Some Linear Operators Preserving Disjoint Support Property
Journal: Sahand Communications in Mathematical Analysis (Vol.18, No. 3)Publication Date: 2021-08-01
Authors : Noha Eftekhari; Ali Bayati Eshkaftaki;
Page : 41-49
Keywords : Disjoint support; Codomain; Linear preserver; Isometry;
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.
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