This article is cited in 4 papers

Representations of $C^*$-algebras in spaces with indefinite metric

V. S. Shulman


Abstract: The problem is considered of orthogonalization of $J$-symmetric representations of $C^*$-algebras in the Pontryagin spaces $\Pi_\varkappa$. It is proved that in spaces with finite rank of indefiniteness, every such representation is similar to a $*$-representation in a Hilbert space. Necessary and sufficient conditions are established for the existence of an invariant dual pair of subspaces for a $J$-symmetric operator algebra.

UDC: 519.5

Received: 24.03.1976

 English version: Mathematical Notes, 1977, 22:4, 816–820

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