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On unitary equivalence of bilateral operator valued weighted shifts

Kośmider Jakub

Opuscula Mathematica

2019

Vol. 39, no. 4

543--555

We establish a characterization of unitary equivalence of two bilateral operator valued weighted shifts with quasi-invertible weights by an operator of diagonal form. We provide an example of unitary equivalence between shifts with weights defined on C2 which cannot be given by any unitary operator of diagonal form. The paper also contains some remarks regarding unitary operators that can give unitary equivalence of bilateral operator valued weighted shifts.

Crossed product of a C*-algebra by a semigroup of interactions

Kwaśniewski B. K.

Demonstratio Mathematica

2014

Vol. 47, nr 2

352--370

The paper presents a construction of the crossed product of a C*-algebra by a commutative semigroup of bounded positive linear maps generated by partial isometries. In particular, it generalizes Antonevich, Bakhtin, Lebedev’s crossed product by an endomorphism, and is related to Exel’s interactions. One of the main goals is the Isomorphism Theorem established in the case of actions by endomorphisms.

On the decomposition of families of quasinormal operators

Burdak Z.

Opuscula Mathematica

2013

Vol. 33, no. 3

419--438

The canonical injective decomposition of a jointly quasinormal family of operators is given. Relations between the decomposition of a quasinormal operator T and the decomposition of a partial isometry in the polar decomposition of T are described. The decomposition of pairs of commuting quasinormal partial isometries and its applications to pairs of commuting quasinormal operators is shown. Examples are given.

Weighted substitution operators between Lp -spaces of vector-valued functions

Raj K., Sharma S. K.

Fasciculi Mathematici

2011

Nr 47

63--70

In this paper we characterize weighted substitution operators between Lp-spaces of vector-valued functions and also make an attempt to characterize isometry and partial isometry of these operators