Fejer's approximation of continuous functions of unitary operators

• Autorzy: Zajkowski K.
• Języki publikacji: EN

Abstrakty

EN

This paper is concerned with a certain aspect of the spectral theory of unitary operators in a Hilbert space and its aim is to give an explicit construction of continuous functions of unitary operators. Starting from a given unitary operator we give a family of sequences of trigonometric polynomials converging weakly to the complex measures which allow us to define functions of the operator.

Słowa kluczowe

EN

spectral theorem for unitary operators; Fejer theorem; Riesz representation theorem; Borel measures; weak-star convergence; *-homomorphism of C*-algebras

• Wydawca: Polskie Towarzystwo Matematyczne
• Czasopismo: Annales Societatis Mathematicae Polonae. Seria 1: Commentationes Mathematicae
• Rocznik: 2002
• Tom: [Z] 42(2)
• Strony: 261--267
• Opis fizyczny: Bibliogr. 5 poz.

Twórcy

autor

Zajkowski K.

• Institute of Mathematics, University of Bialystok, Akademicka 2, 15-267 Bialystok, Poland,

Bibliografia

• [1] N. I. Akhiezer, I. M. Glazman, Theory of linear operators in Hilbert space, Pitman, Boston-London-Melbourne, (1981).
• [2] A. Alexiewicz, Functional Analysis, Warszawa, (1969) (in Polish).
• [3] K. Hoffman, Banach Spaces of Analytic Functions, Prentice-Hall Inc., Englewood Cliffs, N. I., (1962).
• [4] H. Leifelder, A geometric proof of the spectral theorem for unbounded selfadjoint operators, Math. Ann. 242 (1979), 85-96.
• [5] K. Yosida, Functional Analysis, Berlin, (1965).