Vasilescu-Martinelli formula for operators in Banach spaces

• Autorzy: V. Kordula , V. Müller
• Języki publikacji: EN

Abstrakty

EN

We prove a formula for the Taylor functional calculus for functions analytic in a neighbourhood of the splitting spectrum of an n-tuple of commuting Banach space operators. This generalizes the formula of Vasilescu for Hilbert space operators and is closely related to a recent result of D. W. Albrecht.

Kategorie tematyczne

• 47A13: Several-variable operator theory (spectral, Fredholm, etc.)
• 47A60: Functional calculus

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Studia Mathematica
• Rocznik: 1995
• Tom: 113
• Numer: 2
• Strony: 127-139

Daty

wydano

1995

otrzymano

1994-02-25

poprawiono

1994-06-28

Twórcy

autor

V. Kordula

• Institute of Mathematics, Academy of Sciences of the Czech Republic, Žitná 25, 115 67 Praha 1, Czech Republic

autor

V. Müller

• Institute of Mathematics, Academy of Sciences of the Czech Republic, Žitná 25, 115 67 Praha 1, Czech Republic

Bibliografia

• [1] D. W. Albrecht, Integral formulae for special cases of Taylor's functional calculus, Studia Math. 105 (1993), 51-68.
• [2] K. Laursen and M. Mbekhta, Closed range multipliers and generalized inverses, ibid. 107 (1993), 127-135.
• [3] R. Levi, Notes on the Taylor joint spectrum of commuting operators, in: Spectral Theory, Banach Center Publ. 8, PWN-Polish Scientific Publishers, Warszawa, 1982, 321-332.
• [4] J. L. Taylor, A joint spectrum for several commuting operators, J. Funct. Anal. 6 (1970), 172-191.
• [5] J. L. Taylor, Analytic-functional calculus for several commuting operators, Acta Math. 125 (1970), 1-38.
• [6] F.-H. Vasilescu, A Martinelli type formula for the analytic functional calculus, Rev. Roumaine Math. Pures Appl. 23 (1978), 1587-1605.
• [7] F.-H. Vasilescu, A multidimensional spectral theory in C*-algebras, in: Spectral Theory, Banach Center Publ. 8, PWN-Polish Scientific Publishers, Warszawa, 1982, 471-491.
• [8] F.-H. Vasilescu, Calcul Funcţional Analitic Multidimensional, Editura Academiei, Bucureşti, 1979.