Advertisement

Integral Equations and Operator Theory

, Volume 21, Issue 4, pp 383–429 | Cite as

m-Isometric transformations of Hilbert space, I

  • Jim Agler
  • Mark Stankus
Article

AMS subject classification

31C25 46E20 46F05 46F10 46F20 47A20 47A45 47A55 47B3 47N30 60G99 60K99 
This is a preview of subscription content, log in to check access.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. [Ag1] Agler, J.,Subjordan operators, Thesis, Indiana University, 1980.Google Scholar
  2. [Ag2] Agler, J., “The Arveson extension theorem and coanalytic models”,Integral Equations and Operator Theory 5 (1982), 608–631.Google Scholar
  3. [Ag3] Agler, J.,An Abstract Approach to Model Theory, Surveys of some recent results in operator theory Vol2, Pitman Research Notes in Mathematics Series; ISSN 0269-3674;192, 1–24.Google Scholar
  4. [Ag4] Agler, J., “A Disconjugacy Theorem for Toeplitz Operators”,American Journal of Mathematics,112(1990), 1–14.Google Scholar
  5. [Ag5] Agler, J., “Sub-Jordan Operators Bishop's Theorem, Spectral Inclusion and Spectral Sets”,J. Operator Theory 7(1982), 373–395.Google Scholar
  6. [Ag6] Agler, J., “Hypercontractions and Subnormality”,J. Operator Theory 13(1985), 203–217.Google Scholar
  7. [Ag7] Agler, J., “Rational Dilation of an annulus”,Annals of Mathematics,121(1985), 537–563.Google Scholar
  8. [Arv1] Arveson, W.B., “Subalgebras ofC *-algebras”,Acta Math. 123(1969), 141–224.Google Scholar
  9. [Arv2] Arveson, W.B., “Subalgebras ofC *-algebras II”,Acta Math. 128(1972), 271–308.Google Scholar
  10. [B] Beurling, A., “On two problems concerning Linear transformations in Hilbert space”,Acta. Math. 81 (1949), 239–255.Google Scholar
  11. [Ber-S] Berger, C.A., Shaw, B.L., “Self-commutators of multicyclic hyponormal operators are always trace class”, B.A.M.S.,79 (1973), 1193–1199.Google Scholar
  12. [Bir-S] Birman, M. S., and Solomjak, M. Z.,Spectral Theory of self-adjoint Operators in Hilbert Space, D. Reidel Publishing Company, Dordrecht/Boston/Lancaster/Tokyo, 1986.Google Scholar
  13. [Br-R] de Branges, L., Rovnyak, J.,Square Summable Power Series, New York, Holt, Rinehart and Winston, 1966.Google Scholar
  14. [C] Conway, John B.,A Course in Functional Analysis, New York/Berlin/Heidelberg/Tokyo, Springer-Verlag, 1985.Google Scholar
  15. [Ca] Calkin, J.W., “Two-sided ideals and congruences in the ring of bounded operators in Hilbert space”,Ann. of Math. (2)42(1941), 839–873.Google Scholar
  16. [C-F] Colojoară, I., Foias C.,Theory of Generalized spectral Operators New York, Gordon and Breach, 1968.Google Scholar
  17. [C-P] Curto, R.E. and Putinar, M., “Existence of non-subnormal polynomially hyponormal operators”, B.A.M.S.,25(1991) #2, 373–378.Google Scholar
  18. [F] Fillmore, P. A.,Notes on operator theory, New York, Van Nostrand, 1970.Google Scholar
  19. [Fr] Franks, E.,Polynomially subnormal operator tuples, Thesis, University of California, San Diego, 1991.Google Scholar
  20. [Ha] Halmos, P.R.,A Hilbert space problem book, Princeton, D. Van Nostrand, 1970.Google Scholar
  21. [H1] Helton, J. W., “Operators with a representation as multiplication byx on a Sobolev space”,Colloquia Math. Soc. Janos Bolyai 5, Hilbert Space Operators, Tihany, Hungary (1970), 279–287.Google Scholar
  22. [H2] Helton, J. W., “Infinite dimensional Jordan operators and Sturm-Liouville conjugate point theory”,Trans. Amer. Math. Soc. 170 (1972), 305–331.Google Scholar
  23. [H3] Helton, J. W.,Operator Theory, analytic functions, matrices, and electrical engineering, Conference Board of the Mathematical Sciences by the American Mathematical Society, 1987.Google Scholar
  24. [Hel] Helson, H.,Lectures on Invariant Subspaces, New York, Academic Press, 1964.Google Scholar
  25. [M1] McCullough, S.A.,3-isometries, Thesis, University of California, San Diego, 1987.Google Scholar
  26. [M2] McCullough, S.A., “SubBrownian Operators”,J. Operator Theory,22(1989) 2, 291–305.Google Scholar
  27. [M-G] Boutet de Monvel and V. Guillemin,The spectral theory of Toeplitz operators, Princeton University Press, Princeton N.J., University of Tokyo Press, Tokyo, 1981.Google Scholar
  28. [N] Nielsen, O.A., “Direct Integral Theory”,Lecture notes in pure and applied mathematics, vol.61, Marcel Dekker, Inc, New York and Basel, 1980.Google Scholar
  29. [P] Putnam, C.R., “An inequality for the area of hyponormal spectra”,Math. Z.,116(1970), 323–330.Google Scholar
  30. [R1] Richter, S., “Invariant subspaces of the Dirichlet shift”,J. reine agnew. Math. 386 (1988), 205–220.Google Scholar
  31. [R2] Richter, S., “A representation theorem for cyclic analytic two-isometries”,Trans. Amer. Math. Soc., to appear.Google Scholar
  32. [Sa] Sarason, D., “Doubly shift-invariant spaces inH 2”,J. Operator Theory 16 (1986), 75–97.Google Scholar
  33. [Steg] Stegenga, D.A., “Multipliers of Dirichlet space”, Ill.Jour. of Math. 24(1980), 113–139.Google Scholar
  34. [St] Stankus, M.,Isosymmetric Linear Transformations On Complex Hilbert Space, Thesis, University of California, San Diego, 1993.Google Scholar
  35. [Sti] Stinespring, W.F., “Positive functions onC *-algebras”, P.A.M.S.6(1955), 211–216.Google Scholar
  36. [Sz.-N,F] Sz.-Nagy. Foias, C.,Harmonic analysis of operators in Hilbert space, North Holland, Amsterdam, 1970.Google Scholar

Copyright information

© Birkhäuser Verlag 1995

Authors and Affiliations

  • Jim Agler
    • 1
  • Mark Stankus
    • 1
  1. 1.Department of MathematicsUniv. Of Calif.San Diego, La JollaUSA

Personalised recommendations

Cite article

Buy options