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On operators generating conditional bases in a Hilbert space


A spectral characterization is given to the linear operators which in a Hilbert space transform some complete orthonormal system into a conditional basis.

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Translated from Matematicheskie Zametki, Vol. 12, No, 1, pp. 73–84, July, 1972.

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Olevskii, A.M. On operators generating conditional bases in a Hilbert space. Mathematical Notes of the Academy of Sciences of the USSR 12, 476–482 (1972).

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  • Hilbert Space
  • Linear Operator
  • Orthonormal System
  • Spectral Characterization
  • Complete Orthonormal System