The numerical radius of a commuting product (Q583573)
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scientific article; zbMATH DE number 4132935
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | The numerical radius of a commuting product |
scientific article; zbMATH DE number 4132935 |
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The numerical radius of a commuting product (English)
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1988
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This paper investigates the long-standing problem: What is the smallest constant C such that \[ w(TS)\leq Cw(T)\| S\| \] for all commuting bounded linear oprators S and T on a complex Hilbert space? Here, \(w(A)=\sup \{| (Ax,x)| /(x,x),\quad x\neq 0\}.\) With the help of a computer, the author constructs two commuting operators S and T on a 12- dimensional Hilbert space such that \(c>1.01\).
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