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Representations of relations connecting a collection of commuting self-adjoint operators with a non-self-adjoint one

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Abstract

We consider a collection of self-adjoint commuting operators A=An, nεN∼(N), which are connected with a non-self-adjoint operator B by relations of the form AnB=BFn(A),nεN, under the condition imposed on B of the formB * B-F0 (BB*, A). We prove that the problem of description of representations of such relations can be reduced to the case of a unitary B.

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Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 42, No. 9, pp. 1258–1262, September, 1990.

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Vaisleb, É.E. Representations of relations connecting a collection of commuting self-adjoint operators with a non-self-adjoint one. Ukr Math J 42, 1119–1123 (1990). https://doi.org/10.1007/BF01056608

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