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Measures on spaces of operators and isometries. (Russian. English summary) Zbl 0606.46030

Let \(\mu\) be a finite Borel (in the strong operator topology) measure on the space B(E,F) of bounded linear operators from E into F; E, F being Banach spaces. Suppose that either \(E=C(K)\), F arbitrary, \(p>1\) or \(E=F=L^ q(Y)\), \(p>1\), \(q>1\), \(q\not\in [p,2]\). Suppose next that \(\| e\|^ p=\int \| Te\|^ pd\mu (T)\) for every \(e\in E\). Then \(\mu\) is supported on scalar multiples of isometries.

MSC:

46G12 Measures and integration on abstract linear spaces
28C20 Set functions and measures and integrals in infinite-dimensional spaces (Wiener measure, Gaussian measure, etc.)
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