6533b859fe1ef96bd12b78b4
RESEARCH PRODUCT
New spaces of matrices with operator entries
Ismael García-bayonaOscar Blascosubject
Discrete mathematicsClass (set theory)010102 general mathematics010103 numerical & computational mathematicsSpace (mathematics)01 natural sciencesToeplitz matrixFunctional Analysis (math.FA)Mathematics - Functional AnalysisMathematics (miscellaneous)Operator (computer programming)FOS: Mathematics47L10 46E40 (Primary) 47A56 15B05 46G10 (Secondary)Hadamard product0101 mathematicsVector-valued functionComputer Science::DatabasesSeparable hilbert spaceMathematicsSchur multiplierdescription
In this paper, we will consider matrices with entries in the space of operators $\mathcal{B}(H)$, where $H$ is a separable Hilbert space and consider the class of matrices that can be approached in the operator norm by matrices with a finite number of diagonals. We will use the Schur product with Toeplitz matrices generated by summability kernels to describe such a class and show that in the case of Toeplitz matrices it can be identified with the space of continuous functions with values in $\mathcal B(H)$. We shall also introduce matriceal versions with operator entries of classical spaces of holomorphic functions such as $H^\infty(\mathbb{D})$ and $A(\mathbb{D})$ when dealing with upper triangular matrices.
| year | journal | country | edition | language |
|---|---|---|---|---|
| 2019-04-17 |