\(\mathbb{A}\)-Berezin number inequalities for \(2\times 2\) operator matrices. (English) Zbl 07873947
Summary: Let \(\mathbb{A}\) be the \(2\times 2\) diagonal operator matrix determined by a positive Hilbert space operator \(A\). We give several upper bounds for the \(\mathbb{A}\)-Berezin number of \(2\times 2\) block matrices on a reproducing kernel Hilbert space and prove inequalities for the \(A\)-Berezin number of Hilbert space operators. Our results in this paper generalize and refine earlier the \(A\)-Berezin number inequalities.
MSC:
| 47A05 | General (adjoints, conjugates, products, inverses, domains, ranges, etc.) |
| 46C05 | Hilbert and pre-Hilbert spaces: geometry and topology (including spaces with semidefinite inner product) |
| 47B65 | Positive linear operators and order-bounded operators |
| 47A30 | Norms (inequalities, more than one norm, etc.) of linear operators |
| 46E22 | Hilbert spaces with reproducing kernels (= (proper) functional Hilbert spaces, including de Branges-Rovnyak and other structured spaces) |
| 15A60 | Norms of matrices, numerical range, applications of functional analysis to matrix theory |
Keywords:
positive operator; operator matrix; semi-inner product; reproducing kernel Hilbert space; \(A\)-Berezin symbol; inequalityReferences:
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