EMIS ELibM Electronic Journals PUBLICATIONS DE L'INSTITUT MATHÉMATIQUE (BEOGRAD) (N.S.)
Vol. 46(60), pp. 141--144 (1989)

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A characterization of formally symmetric unbounded operators

Danko Joci\'c

Matematicki fakultet, Beograd, Yugoslavia

Abstract: We give necessary and sufficient conditions for an operator in a Hilbert space to be formally symmetric, symmetric or self-adjoint. This generalizes the well-known fact that a bounded operator $T$ is self-adjoint if and only if $T^\ast T\le(\operatorname{Re}T)^2$. The proof is based on a well-behaved extension of the corresponding symmetric operator.

Classification (MSC2000): 47B25

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Electronic fulltext finalized on: 2 Nov 2001. This page was last modified: 16 Nov 2001.

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