Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)



Automorphisms and tensor products of algebras

Author: John W. Bunce
Journal: Proc. Amer. Math. Soc. 44 (1974), 93-95
MSC: Primary 46H20
MathSciNet review: 0331063
Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract: In this note we prove that if $ A$ is a complex Banach algebra with identity, then the automorphism on $ A\hat \otimes A$ determined by $ \theta (a \otimes b) = b \otimes a$ is inner if and only if $ A = {M_n}(C)$.

References [Enhancements On Off] (What's this?)

  • [1] B. Gelbaum, Tensor products of Banach algebra, Canad. J. Math. 11 (1959), 297-310. MR 21 #2922. MR 0104162 (21:2922)
  • [2] I. N. Herstein, Noncommutative rings, Carus Mathematical Monograph, no. 15, Mathematical Association of America; distributed by Wiley, New York, 1968. MR 37 #2790. MR 0227205 (37:2790)
  • [3] S. Sakai, Automorphisms and tensor products of operator algebras, Amer. J. Math. (to appear). MR 0390787 (52:11610)
  • [4] R. Schatten, A theory of cross-spaces, Ann. of Math. Studies, no. 26, Princeton Univ. Press, Princeton, N.J., 1950. MR 12, 186. MR 0036935 (12:186e)
  • [5] F. Treves, Topological vector spaces, distributions and kernels, Academic Press, New York, 1967. MR 37 #726. MR 0225131 (37:726)
  • [6] K. Yosida, Functional analysis, 2nd ed., Die Grundlehren der math. Wissenschaften, Band 123, Academic Press, New York; Springer-Verlag, Berlin and New York, 1968. MR 39 #741. MR 0239384 (39:741)

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 46H20

Retrieve articles in all journals with MSC: 46H20

Additional Information

Keywords: Banach algebra, tensor product, automorphism
Article copyright: © Copyright 1974 American Mathematical Society

American Mathematical Society