Isometries of CSL algebras

Solel, Baruch

doi:10.1090/S0002-9947-1992-1053117-5

Isometries of CSL algebras
HTML articles powered by AMS MathViewer

by Baruch Solel

Trans. Amer. Math. Soc. 332 (1992), 595-606

DOI: https://doi.org/10.1090/S0002-9947-1992-1053117-5

PDF | Request permission

Abstract:

We show that every Jordan isomorphism of $\text {CSL}$ algebras, whose restriction to the diagonal of the algebra is a selfadjoint map, is the sum of an isomorphism and an anti-isomorphism. It follows that every surjective linear isometry of $\text {CSL}$ algebras is the sum of an isomorphism and an anti-isomorphism, followed by a unitary multiplication.

References

Jonathan Arazy and Baruch Solel, Isometries of nonselfadjoint operator algebras, J. Funct. Anal. 90 (1990), no. 2, 284–305. MR 1052336, DOI 10.1016/0022-1236(90)90085-Y
William Arveson, Operator algebras and invariant subspaces, Ann. of Math. (2) 100 (1974), 433–532. MR 365167, DOI 10.2307/1970956
Kenneth R. Davidson, Nest algebras, Pitman Research Notes in Mathematics Series, vol. 191, Longman Scientific & Technical, Harlow; copublished in the United States with John Wiley & Sons, Inc., New York, 1988. Triangular forms for operator algebras on Hilbert space. MR 972978

Isometric automorphisms and homology for non-self-adjoint operator algebras

Frank Gilfeather and Robert L. Moore, Isomorphisms of certain CSL algebras, J. Funct. Anal. 67 (1986), no. 2, 264–291. MR 845200, DOI 10.1016/0022-1236(86)90039-X
Richard V. Kadison, Isometries of operator algebras, Ann. of Math. (2) 54 (1951), 325–338. MR 43392, DOI 10.2307/1969534

Fundamentals of the theory of operator algebras

Cecelia Laurie and W. E. Longstaff, A note on rank-one operators in reflexive algebras, Proc. Amer. Math. Soc. 89 (1983), no. 2, 293–297. MR 712641, DOI 10.1090/S0002-9939-1983-0712641-2
R. L. Moore and T. T. Trent, Isometries of nest algebras, J. Funct. Anal. 86 (1989), no. 1, 180–209. MR 1013938, DOI 10.1016/0022-1236(89)90069-4

Isometries of certain reflexive operator algebras