Conditionally multiplicative maps on the set of all bounded observables preserving compatibility

Linear Maps on the Space of All Bounded Observables Preserving Maximal Deviation

In this paper we determine all the bijective linear maps on the space of bounded observables which preserve a fixed moment or the variance. Nonlinear versions of the corresponding results are also presented.

Order-automorphisms of the Set of Bounded Observables

Let H be a complex Hilbert space and denote by Bs(H) the set of all self-adjoint bounded linear operators on H . In this paper we describe the form of all bijective maps (no linearity or continuity is assumed) on Bs(H) which preserve the order ≤ in both directions.

Multiplicative bijective maps on standard operator algebras

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...

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...