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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 trigonometric-like decompositions of functions with respect to the cyclic group of order n

Kwaśniewski A. K., Kwaśniewski B. K.

Journal of Applied Analysis

2002

Vol. 8, nr 1

111-127

The cyclic group labelled family of α-projection operators implicitly present in [28] is used as in [5]-[9], [23] for investigation of decomposition of functions with respect to the cyclic group of order n. Series of new identities thus arising are demonstrated and new perspectives for further investigation are indicated as for example in the case of q-extended special polynomials. The paper constitutes an example of the application of the method of projections introduced in [26]; see also references [5]-[9].