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Toeplitz operators on Bergman spaces and Hardy multipliers

Wolfgang Lusky, Jari Taskinen (2011)

Studia Mathematica

We study Toeplitz operators T a with radial symbols in weighted Bergman spaces A μ p , 1 < p < ∞, on the disc. Using a decomposition of A μ p into finite-dimensional subspaces the operator T a can be considered as a coefficient multiplier. This leads to new results on boundedness of T a and also shows a connection with Hardy space multipliers. Using another method we also prove a necessary and sufficient condition for the boundedness of T a for a satisfying an assumption on the positivity of certain indefinite...

Toeplitz Quantization for Non-commutating Symbol Spaces such as S U q ( 2 )

Stephen Bruce Sontz (2016)

Communications in Mathematics

Toeplitz quantization is defined in a general setting in which the symbols are the elements of a possibly non-commutative algebra with a conjugation and a possibly degenerate inner product. We show that the quantum group S U q ( 2 ) is such an algebra. Unlike many quantization schemes, this Toeplitz quantization does not require a measure. The theory is based on the mathematical structures defined and studied in several recent papers of the author; those papers dealt with some specific examples of this new...

Toeplitz-Berezin quantization and non-commutative differential geometry

Harald Upmeier (1997)

Banach Center Publications

In this survey article we describe how the recent work in quantization in multi-variable complex geometry (domains of holomorphy, symmetric domains, tube domains, etc.) leads to interesting results and problems in C*-algebras which can be viewed as examples of the "non-commutative geometry" in the sense of A. Connes. At the same time, one obtains new functional calculi (of pseudodifferential type) with possible applications to partial differential equations and group representations.

Topologies on the group of invertible transformations

Maciej Burnecki, Robert Rałowski (2011)

Banach Center Publications

We enlarge the amount of embeddings of the group G of invertible transformations of [0,1] into spaces of bounded linear operators on Orlicz spaces. We show the equality of the inherited coarse topologies.

Towards a theory of some unbounded linear operators on p -adic Hilbert spaces and applications

Toka Diagana (2005)

Annales mathématiques Blaise Pascal

We are concerned with some unbounded linear operators on the so-called p -adic Hilbert space 𝔼 ω . Both the Closedness and the self-adjointness of those unbounded linear operators are investigated. As applications, we shall consider the diagonal operator on 𝔼 ω , and the solvability of the equation A u = v where A is a linear operator on 𝔼 ω .

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