Spectrum of a linear operator in a family of banach spaces containing Hilbert space

V. V. Shevchik

Simferopol State University

Abstract: The mutual relation is established between the spectra of a bounded linear operator acting in a family of Banach spaces. It is assumed in addition that one of the spaces is a Hilbert space and that the operator acting on it is self-adjoint. An example is presented illustrating the properties proved.

UDC: 513.8

Received: 03.10.1975

 English version: Mathematical Notes, 1977, 22:3, 767–769

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