Linear maps preserving A-unitary operators

Unitary Operators Preserving Wavelets

We characterize a special class of unitary operators that preserve orthonormal wavelets. In the process we also prove that symmetric wavelet sets cover the real line.

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...

Spectrum Preserving Linear Maps Between Banach Algebras

In this paper we show that if A is a unital Banach algebra and B is a purely innite C*-algebra such that has a non-zero commutative maximal ideal and $phi:A rightarrow B$ is a unital surjective spectrum preserving linear map. Then $phi$ is a Jordan homomorphism.

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...