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Toeplitz operators associated with analytic crossed products

Published online by Cambridge University Press:  24 October 2008

Kichi-Suke Saito
Affiliation:
Department of Mathematics, Faculty of Science, Niigata University, Niigata, 950-21, Japan

Extract

The class of Toeplitz operators has attracted the attention of several mathematicians and plays an important part in operator theory and related fields. Here we have a special interest in connection with the theory of shift operators, Toeplitz operators, and Hardy classes of vector and operator valued functions as in [12].

Type
Research Article
Copyright
Copyright © Cambridge Philosophical Society 1990

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References

REFERENCES

[1]Arveson, W. B.. Analyticity in operator algebras. Amer. J. Math. 89 (1967), 578642.Google Scholar
[2]Brown, A. and Halmos, P. R.. Algebraic properties of Toeplitz operators. J. Reine Angew. Math. 213 (1964), 89102.Google Scholar
[3]Douglas, R. G.. Banach Algebra Techniques in Operator Theory (Academic Press, 1972).Google Scholar
[4]Douglas, R. G.. Banach Algebras Techniques in the Theory of Toeplitz Operators. Regional Conference Series in Mathematics no. 15 (American Mathematical Society, 1973).Google Scholar
[5]Haagerup, U.. The standard form of von Neumann algebras. Math. Scand. 37 (1975), 271283.Google Scholar
[6]Loebl, R. I. and Muhly, P. S.. Analyticity and flows in von Neumann algebras. J. Funct. Anal. 29 (1978), 214252.Google Scholar
[7]McAsey, M., Muhly, P. S. and Saito, K.-S.. Nonselfadjoint crossed products (Invariant subspaces and maximality). Trans. Amer. Math. Soc. 248 (1979), 381409.Google Scholar
[8]McAsey, M., Muhly, P. S. and Saito, K.-S.. Nonselfadjoint crossed products II. J. Math. Soc. Japan 33 (1981), 485495.Google Scholar
[9]McAsey, M., Muhly, P. S. and Saito, K.-S.. Nonselfadjoint crossed products III (Infinite algebras). J. Operator Theory 12 (1984), 322.Google Scholar
[10]Muhly, P. S. and Saito, K.-S.. Analytic crossed products and outer conjugacy classes of automorphisms of von Neumann algebras. Math. Scand. 58 (1986), 5568.Google Scholar
[11]Muhly, P. S. and Saito, K.-S.. Analytic crossed products and outer conjugacy classes of automorphisms of von Neumann algebras II. Math. Ann. 279 (1987), 17.Google Scholar
[12]Rosenblum, M. and Rovnyak, J.. Hardy Classes and Operator Theory. Oxford Math. Monographs (Oxford University Press, 1985).Google Scholar
[13]Saito, K.-S.. The Hardy spaces associated with a periodic flow on a von Neumann algebra. Tohokû Math. J. 29 (1977), 6975.Google Scholar
[14]Saito, K.-S.. A note on invariant subspaces for finite maximal subdiagonal algebras. Proc. Amer. Math. Soc. 77 (1979), 348352.Google Scholar
[15]Saito, K.-S.. Automorphisms and nonselfadjoint crossed products. Pacific J. Math. 102 (1982), 179187.Google Scholar
[16]Solel, B.. The invariant subspace structure of nonselfadjoint crossed products. Trans. Amer. Math. Soc. 279 (1983), 825840.Google Scholar
[17]Solel, B.. Analytic operator algebras (Factorization and an expectation). Trans. Amer. Math. Soc. 287 (1985), 799817.Google Scholar
[18]Terp, M.. L p spaces associated with von Neumann algebras. Rapport (1981).Google Scholar
[19]Toeplitz, O.. Zur Theorie der quadratischen Formen von unendlich vielen Veranderlichen. Math. Ann. 70 (1911), 351376.Google Scholar