Generalized finite operators

• Autorzy: Mecheri S.
• Języki publikacji: EN

Abstrakty

EN

Let B(H) be the algebra of all bounded linear operators on an infinite dimensional complex and separable Hilbert space H. A infinity B(H) is called finite if \\AX - XA - I\\ > 1, VX infinity B(H). In this paper we extend the class of finite operators to a more general class of pairs of operators called generalized finite operators defined by {(A, B) infinity B(H) x B(H) : \\AX - XB - I\\ > 1, VX infinity B(H)} and we present some pairs of generalized finite operators.

Słowa kluczowe

EN

finite operators; generalized derivation; Hilbert space

PL

operatory skończone; pochodne; przestrzeń Hilberta

• Wydawca: De Gruyter
• Czasopismo: Demonstratio Mathematica
• Rocznik: 2005
• Tom: Vol. 38, nr 1
• Strony: 163--167
• Opis fizyczny: Bibliogr. 5 poz.

Twórcy

autor

Mecheri S.

• King Saud University College of Science, Department of Mathematics, P.O. Box 2455, Riyadh 11451, Saudi Arabia

Bibliografia

• [1] J. H. Anderson and C. Foias, Properties which normal operator share with normal derivation and related operators, Pacific J. Math. (1973), 313-325.
• [2] L. A. Fialkow, A note on the operator X→AX−XB, Trans. Amer. Math. Soc. 243 (1978), 147-168.
• [3] P. A. Filmore, J. G. Stampfli, J. P. Williams, On the essential numerical range, the essential spectrum and a problem of Halmos, Acta. Sci. Math. 33 (1972), 179-192.
• [4] S. Mecheri, Finite operators, Demonstratio Math. 37 (2002), 357-366.
• [5] J. P. Williams, Finite operators, Proc. Amer. Math. Soc. 26 (1970), 129-135.