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A remark on complemented subspaces of unitary matrix spaces

Author: Jonathan Arazy
Journal: Proc. Amer. Math. Soc. 79 (1980), 601-608
MSC: Primary 47D15; Secondary 46A45
MathSciNet review: 572312
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Abstract: Theorem A. Let P be a bounded projection in a unitary matrix space $ {C_E}$. Then either $ P{C_E}$ or $ (I - P){C_E}$ contains a subspace which is isomorphic to $ {C_E}$ and complemented in $ {C_E}$.

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  • [3] I. C. Gohberg and M. G. Kreĭn, Introduction to the theory of linear nonselfadjoint operators, Translated from the Russian by A. Feinstein. Translations of Mathematical Monographs, Vol. 18, American Mathematical Society, Providence, R.I., 1969. MR 0246142
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  • [6] Joram Lindenstrauss and Lior Tzafriri, Classical Banach spaces, Lecture Notes in Mathematics, Vol. 338, Springer-Verlag, Berlin-New York, 1973. MR 0415253

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Keywords: Unitary matrix spaces, symmetric sequence spaces, compact operators on Hilbert spaces, complemented subspaces, $ {C_p}$-spaces
Article copyright: © Copyright 1980 American Mathematical Society