Linear maps strongly preserving Moore-Penrose invertibility

Linear maps preserving or strongly preserving majorization on matrices

For $A,Bin M_{nm},$ we say that $A$ is left matrix majorized (resp. left matrix submajorized) by $B$ and write $Aprec_{ell}B$ (resp. $Aprec_{ell s}B$), if $A=RB$ for some $ntimes n$ row stochastic (resp. row substochastic) matrix $R.$ Moreover, we define the relation $sim_{ell s} $ on $M_{nm}$ as follows: $Asim_{ell s} B$ if $Aprec_{ell s} Bprec_{ell s} A.$ This paper characterizes all linear p...

A Survey of Invertibility and Spectrum Preserving Linear Maps

linear maps preserving or strongly preserving majorization on matrices

for $a,bin m_{nm},$ we say that $a$ is left matrix majorized (resp. left matrix submajorized) by $b$ and write $aprec_{ell}b$ (resp. $aprec_{ell s}b$), if $a=rb$ for some $ntimes n$ row stochastic (resp. row substochastic) matrix $r.$ moreover, we define the relation $sim_{ell s} $ on $m_{nm}$ as follows: $asim_{ell s} b$ if $aprec_{ell s} bprec_{ell s} a.$ this paper characterizes all linear p...

Invertibility Preserving Linear Maps of Banach Algebras

This talk discusses a conjecture of R. V. Kadison and myself. Our conjecture is that each one-to-one linear map of one unital C*-algebra onto another that preserves the identity is a Jordan isomorphism if it maps the invertible elements of the first C*-algebra onto the invertible elements of the other C*-algebra. Connections are shown between this conjecture and Cartan’s uniqueness theorem. 1. ...

On strongly Jordan zero-product preserving maps

In this paper, we give a characterization of strongly Jordan zero-product preserving maps on normed algebras as a generalization of  Jordan zero-product preserving maps. In this direction, we give some illustrative examples to show that the notions of strongly zero-product preserving maps and strongly Jordan zero-product preserving maps are completely different. Also, we prove that the direct p...