Download PDF - On operators with unitary ϱ-dilationsAll rights reserved. Copyright exceptions and limitations apply

ArticleOriginal scientific text

Title

On operators with unitary ϱ-dilations

Authors 1, 2

Affiliations

  1. Faculty of Economics, Hokusei Gakuen University, Atsubetsu-ku, Sapporo 004, Japan
  2. Department of Mathematics, Hokkaido University, Sapporo 060, Japan

Abstract

We show a polynomially boundend operator T is similar to a unitary operator if there is a singular unitary operator W and an injection X such that XT = WX. If, in addition, T is of class Cϱ, then T itself is unitary.

Keywords

ENG
polynomially bounded operators, operators of class Cϱ, unitary ϱ-dilation

Bibliography

  1. K. Hoffman, Banach Spaces of Analytic Functions, Prentice-Hall, Englewood Cliffs, N.J., 1962.
  2. W. Mlak, Algebraic polynomially bounded operators, Ann. Polon. Math. 29 (1974), 103-109.
  3. W. Mlak, Operator valued representations of function algebras, in: Linear Operators and Approximation II, Proc. Conf. Oberwolfach Math. Res. Inst., Internat. Ser. Numer. Math. 25, Birkhäuser, Basel, 1974, 49-79.
  4. B. Sz.-Nagy, On uniformly bounded linear transformations in Hilbert space, Acta Sci. Math. (Szeged) 11 (1947), 152-157.
  5. B. Sz.-Nagy and C. Foiaş, Harmonic Analysis of Operators on Hilbert Space, North-Holland, Amsterdam, 1970.
  6. H. Watanabe, Operators characterized by certain Cauchy-Schwarz type inequalities, Publ. Res. Inst. Math. Sci. 30 (1994), 249-259.
Annales Polonici Mathematici
1997/66/1
Export to PBN, Opens in new tab
Pages:
11-14
Main language of publication
English
Received
1995-02-15
Published
1997
Exact and natural sciences