A remark on complemented subspaces of unitary matrix spaces
HTML articles powered by AMS MathViewer
- by Jonathan Arazy
- Proc. Amer. Math. Soc. 79 (1980), 601-608
- DOI: https://doi.org/10.1090/S0002-9939-1980-0572312-X
- PDF | Request permission
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 ${C_E}$.References
- Jonathan Arazy, On large subspaces of the Schatten $p$-classes, Compositio Math. 41 (1980), no. 3, 297–336. MR 589085
- 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, DOI 10.1007/BF01682937
- I. C. Gohberg and M. G. Kreĭn, Introduction to the theory of linear nonselfadjoint operators, Translations of Mathematical Monographs, Vol. 18, American Mathematical Society, Providence, R.I., 1969. Translated from the Russian by A. Feinstein. MR 0246142 M. Hall, Jr., Combinational theory, Blaisdell, Waltham, Mass., 1967.
- S. Kwapień and A. Pełczyński, The main triangle projection in matrix spaces and its applications, Studia Math. 34 (1970), 43–68. MR 270118, DOI 10.4064/sm-34-1-43-67
- Joram Lindenstrauss and Lior Tzafriri, Classical Banach spaces, Lecture Notes in Mathematics, Vol. 338, Springer-Verlag, Berlin-New York, 1973. MR 0415253
Bibliographic Information
- © Copyright 1980 American Mathematical Society
- 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