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On Bernstein inequality for vectors in Banach spaces

E. E. Dikarev

Voronezh State University, Voronezh, Russia

Abstract: We obtain the Bernstein inequality for the vectors in the Banach space of the isometric representation of a one-parametric group of the operators. We introduce the notion of an entire at infinity function. For such functions and for the norms of commutation operators we obtain the Bernstein inequality.

Keywords: Banach modulus, isometric representation, Beurling spectrum, entire function, commutation operator.

UDC: 517.9

MSC: 47A10, 47L10

Received: 21.09.2013

 English version: Ufa Mathematical Journal, 2013, 5:4, 75–81

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