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

DOI:
https://doi.org/10.1090/S0002-9939-1980-0572312-X

MathSciNet review:
572312

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Abstract: Theorem A. *Let P be a bounded projection in a unitary matrix space* . *Then either* *or* *contains a subspace which is isomorphic to* *and complemented in* .

**[1]**Jonathan Arazy,*On large subspaces of the Schatten 𝑝-classes*, Compositio Math.**41**(1980), no. 3, 297–336. MR**589085****[2]**Jonathan Arazy,*Some remarks on interpolation theorems and the boundness of the triangular projection in unitary matrix spaces*, Integral Equations Operator Theory**1**(1978), no. 4, 453–495. MR**516764**, https://doi.org/10.1007/BF01682937**[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****[4]**M. Hall, Jr.,*Combinational theory*, Blaisdell, Waltham, Mass., 1967.**[5]**S. Kwapień and A. Pełczyński,*The main triangle projection in matrix spaces and its applications.*, Studia Math.**34**(1970), 43–68. MR**0270118**, https://doi.org/10.4064/sm-34-1-43-67**[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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Additional Information

DOI:
https://doi.org/10.1090/S0002-9939-1980-0572312-X

Keywords:
Unitary matrix spaces,
symmetric sequence spaces,
compact operators on Hilbert spaces,
complemented subspaces,
-spaces

Article copyright:
© Copyright 1980
American Mathematical Society