Commutative C*-Algebras of Toeplitz Operators on Complex Projective Spaces

Toeplitz Operators and Solvable C*-algebras on Hermitian Symmetric Spaces

Bounded symmetric domains (Cartan domains and exceptional domains) are higher-dimensional generalizations of the open unit disc. In this note we give a structure theory for the C*-algebra T generated by all Toeplitz operators Tf(h) := P{fh) with continuous symbol function ƒ G C(S) on the Shilov boundary 5 of a bounded symmetric domain D of arbitrary rank r. Here h belongs to the Hardy space H(S...

Commutative Algebras of Toeplitz Operators on the Bergman Space - Preamble

Preface The book is devoted to the spectral theory of commutative C *-algebras of Toeplitz operators on Bergman spaces, and its applications. For each such commutative algebra we construct a unitary operator which reduces each Toeplitz operator from this algebra to a certain multiplication operator, thus also providing its spectral type representation. This gives us a powerful research tool all...

Commutative C ∗ - algebras of Toeplitz operators and quantization on the unit disk ✩

A family of recently discovered commutative C∗-algebras of Toeplitz operators on the unit disk can be classified as follows. Each pencil of hyperbolic straight lines determines a set of symbols consisting of functions which are constant on the corresponding cycles, the orthogonal trajectories to lines forming a pencil. The C∗-algebra generated by Toeplitz operators with such symbols turns out t...

Toeplitz Operators on Fock Spaces

Absolutely Summing Operators on Non Commutative C-algebras and Applications

Let E be a Banach space that does not contain any copy of l and A be a non commutative C∗-algebra. We prove that every absolutely summing operator from A into E∗ is compact, thus answering a question of Pe lczynski. As application, we show that if G is a compact metrizable abelian group and Λ is a Riesz subset of its dual then every countably additiveA∗-valued measure with bounded variation and...