Symmetry of Banach Algebras1

A Note on the Representations of Nilpotent Lie Algebras1

Banach frames in coorbit spaces consisting of elements which are invariant under symmetry groups

This paper is concerned with the construction of atomic decompositions and Banach frames for subspaces of certain Banach spaces consisting of elements which are invariant under some symmetry group. These Banach spaces – called coorbit spaces – are related to an integrable group representation. The construction is established via a generalization of the well-established Feichtinger-Gröchenig the...

Evolution Equations and Geometric Function Theory in J∗-algebras1

In a series of papers Ky Fan developed a geometric theory of holomorphic functions of proper contractions on Hilbert spaces in the sense of the functional calculus. His results are a powerful tool in the study of the discrete-time semigroups of l-analytic functions defined by iterating such a function on the open unit ball of the space of bounded linear operators on a Hilbert space. In this pap...

A Method for Constructing Dirichlet Algebras1

A Wigner-type Theorem on Symmetry Transformations in Banach Spaces

We obtain an analogue of Wigner’s classical theorem on symmetries for Banach spaces. The proof is based on a result from the theory of linear preservers. Moreover, we present two other Wigner-type results for finite dimensional linear spaces over general fields. Wigner’s theorem on symmetry transformations (sometimes called unitary-antiunitary theorem) plays fundamental role in quantum mechanic...