Abstract
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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K. I. Babenko, “On conjugate functions,” Dokl. Akad. Nauk SSSR,62, No. 2, 157–160 (1948).
A. M. Olevskii, “On an orthonormal system and its applications,” Matem. Sb.,71 (113), No. 3, 297–336 (1966).
V. I. Gurarii and N. I. Gurarii, “On bases in uniformly convex and uniformly smooth Banach spaces,” Izv. Akad. Nauk SSSR, Ser. Matem.,35, 210–215 (1971).
V. F. Gaposhkin, “A generalization of M. Riesz' theorem on conjugate functions,” Matem. Sb.,46 (88), No. 3, 359–372 (1958).
W. Wojtynski, “On conditional bases in non-nuclear Fréchet spaces,” Studia Math.,35, 77–96 (1970).
C. A. McCarthy and J. Schwartz, “On the norm of a finite Boolean algebra of projections, and applications to theorems of Kreiss and Morton,” Comm. Pure Appl. Math.,18, Nos. 1–2, 191–201 (1965).
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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). https://doi.org/10.1007/BF01094395
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DOI: https://doi.org/10.1007/BF01094395