Derivations, homomorphisms, and operator ideals

Author:
T. B. Hoover

Journal:
Proc. Amer. Math. Soc. **62** (1977), 293-298

MSC:
Primary 46L05

MathSciNet review:
0435860

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Abstract | References | Similar Articles | Additional Information

Abstract: Let be a -algebra of operators on a Hilbert space, and let be the Schatten *p*-ideal. It is shown that every derivation from to is inner. A similar argument shows that two -homomorphisms which agree modulo are equivalent.

**[1]**Nelson Dunford and Jacob T. Schwartz,*Linear operators. Part II: Spectral theory. Self adjoint operators in Hilbert space*, With the assistance of William G. Bade and Robert G. Bartle, Interscience Publishers John Wiley & Sons New York-London, 1963. MR**0188745****[2]**Barry Edward Johnson,*Cohomology in Banach algebras*, American Mathematical Society, Providence, R.I., 1972. Memoirs of the American Mathematical Society, No. 127. MR**0374934****[3]**B. E. Johnson and S. K. Parrott,*Operators commuting with a von Neumann algebra modulo the set of compact operators*, J. Functional Analysis**11**(1972), 39–61. MR**0341119****[4]**Richard V. Kadison and John R. Ringrose,*Cohomology of operator algebras. II. Extended cobounding and the hyperfinite case*, Ark. Mat.**9**(1971), 55–63. MR**0318907****[5]**Alan Lambert,*Equivalence for groups and semigroups of operators*, Indiana Univ. Math. J.**24**(1974/75), 879–885. MR**0365225****[6]**I. Namioka and E. Asplund,*A geometric proof of Ryll-Nardzewski’s fixed point theorem*, Bull. Amer. Math. Soc.**73**(1967), 443–445. MR**0209904**, 10.1090/S0002-9904-1967-11779-8**[7]**Shôichirô Sakai,*𝐶*-algebras and 𝑊*-algebras*, Springer-Verlag, New York-Heidelberg, 1971. Ergebnisse der Mathematik und ihrer Grenzgebiete, Band 60. MR**0442701**

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Additional Information

DOI:
http://dx.doi.org/10.1090/S0002-9939-1977-0435860-9

Keywords:
Derivation,
-homomorphism,
operator ideals

Article copyright:
© Copyright 1977
American Mathematical Society