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.
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Translated from Matematicheskie Zametki, Vol. 22, No. 4, pp. 495–498, October, 1977.
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Shevchik, V.V. Spectrum of a linear operator in a family of banach spaces containing Hilbert space. Mathematical Notes of the Academy of Sciences of the USSR 22, 767–769 (1977). https://doi.org/10.1007/BF01146420
- Hilbert Space
- Banach Space
- Linear Operator
- Bounded Linear Operator
- Mutual Relation