Isometries of $^{\ast }$-invariant subspaces
HTML articles powered by AMS MathViewer
- by Arthur Lubin
- Trans. Amer. Math. Soc. 190 (1974), 405-415
- DOI: https://doi.org/10.1090/S0002-9947-1974-0338823-9
- PDF | Request permission
Abstract:
We consider families of increasing $^\ast$-invariant subspaces of ${H^2}(D)$, and from these we construct canonical isometrics from certain ${L^2}$ spaces to ${H^2}$. We give necessary and sufficient conditions for these maps to be unitary, and discuss the relevance to a problem concerning a concrete model theory for a certain class of operators.References
- P. R. Ahern and D. N. Clark, On functions orthogonal to invariant subspaces, Acta Math. 124 (1970), 191–204. MR 264385, DOI 10.1007/BF02394571
- Arne Beurling, On two problems concerning linear transformations in Hilbert space, Acta Math. 81 (1948), 239–255. MR 27954, DOI 10.1007/BF02395019
- Nelson Dunford and Jacob T. Schwartz, Linear operators. Part II: Spectral theory. Self adjoint operators in Hilbert space, Interscience Publishers John Wiley & Sons, New York-London, 1963. With the assistance of William G. Bade and Robert G. Bartle. MR 0188745
- Felix Hausdorff, Set theory, 2nd ed., Chelsea Publishing Co., New York, 1962. Translated from the German by John R. Aumann et al. MR 0141601
- Kenneth Hoffman, Banach spaces of analytic functions, Prentice-Hall Series in Modern Analysis, Prentice-Hall, Inc., Englewood Cliffs, N.J., 1962. MR 0133008
- T. L. Kriete III, A generalized Paley-Wiener theorem, J. Math. Anal. Appl. 36 (1971), 529–555. MR 288275, DOI 10.1016/0022-247X(71)90036-9
- Thomas L. Kriete, Fourier transforms and chains of inner functions, Duke Math. J. 40 (1973), 131–143. MR 328659
- K. Kuratowski, Topology. Vol. I, Academic Press, New York-London; Państwowe Wydawnictwo Naukowe [Polish Scientific Publishers], Warsaw, 1966. New edition, revised and augmented; Translated from the French by J. Jaworowski. MR 0217751
- Arthur Lubin, Extensions of measures and the von Neumann selection theorem, Proc. Amer. Math. Soc. 43 (1974), 118–122. MR 330393, DOI 10.1090/S0002-9939-1974-0330393-X —, Isometries of $^\ast$-invariant subspaces of ${H^2}(D)$, Thesis, University of Wisconsin, Madison, Wis., 1972.
- J. L. Walsh, Interpolation and approximation by rational functions in the complex domain, 3rd ed., American Mathematical Society Colloquium Publications, Vol. XX, American Mathematical Society, Providence, R.I., 1960. MR 0218587
Bibliographic Information
- © Copyright 1974 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 190 (1974), 405-415
- MSC: Primary 47B37; Secondary 47A15
- DOI: https://doi.org/10.1090/S0002-9947-1974-0338823-9
- MathSciNet review: 0338823