ON AUTOMATIC SURJECTIVITY OF SPECTRUM PRESERVING ADDITIVE TRANSFORMATIONS

E.H. El Bouchibti

IJPAM: Volume 112, No. 3 (2017)

Title

ON AUTOMATIC SURJECTIVITY OF SPECTRUM
PRESERVING ADDITIVE TRANSFORMATIONS

Authors

El Houcine El Bouchibti
Polydisciplinary Faculty - Taroudant
Ibno Zohr university
B.P. 271, CP 83000, Hay Lastah Taroudant, MOROCCO

Abstract

Let

and

be an infinite dimensional complex Banach spaces and let $\Phi:B(X)\longrightarrow B(Y)$ be a spectrum preserving additive transformation. We show that if the range of $\Phi$ contains the ideal of finite rank operators of

, then either $\Phi(T)=ATA^{-1}$ or $\Phi(T)=BT^{*}B^{-1}$ for every $T\in B(X)$ , where $A:X\longrightarrow Y$ and $B:X'\longrightarrow Y$ are linear bounded isomorphisms.

History

Received: April 29, 2016
Revised: November 15, 2016
Published: February 9, 2017

AMS Classification, Key Words

AMS Subject Classification: 15A04, 15A86, 47B48, 47B49
Key Words and Phrases: linear preserver problem, trace, operator algebra, analytic functions

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How to Cite?

DOI: 10.12732/ijpam.v112i3.4 How to cite this paper?

Source: International Journal of Pure and Applied Mathematics
ISSN printed version: 1311-8080
ISSN on-line version: 1314-3395
Year: 2017
Volume: 112
Issue: 3
Pages: 489 - 496

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