Axiomatic theory of spectrum III: semiregularities

• Autorzy: Vladimír Müller
• Języki publikacji: EN

Abstrakty

EN

We introduce and study the notions of upper and lower semiregularities in Banach algebras. These notions generalize the previously studied notion of regularity - a class is a regularity if and only if it is both upper and lower semiregularity. Each semiregularity defines in a natural way a spectrum which satisfies a one-way spectral mapping property (the spectrum defined by a regularity satisfies the both-ways spectral mapping property).

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Studia Mathematica
• Rocznik: 2000
• Tom: 142
• Numer: 2
• Strony: 159-169

Daty

wydano

2000

otrzymano

1999-11-22

Twórcy

autor

Vladimír Müller

• Institute of Mathematics AV ČR, Žitná 25, 115 67 Praha 1, Czech Republic

Bibliografia

• [G] S. Grabiner, Uniform ascent and descent of bounded operators, J. Math. Soc. Japan 34 (1982), 317-337.
• [GL] B. Gramsch and D. Lay, Spectral mapping theorems for essential spectra, Math. Ann. 192 (1971), 17-32.
• [H1] R. Harte, On the exponential spectrum in Banach algebras, Proc. Amer. Math. Soc. 58 (1976), 114-118.
• [H2] R. Harte, Fredholm theory relative to a Banach algebra homomorphism, Math. Z. 179 (1982), 431-436.
• [H3] R. Harte, Invertibility and Singularity for Bounded Linear Operators, Marcel Dekker, 1988.
• [K] T. Kato, Perturbation Theory for Linear Operators, Springer, Berlin, 1966.
• [KM] V. Kordula and V. Müller, On the axiomatic theory of spectrum, Studia Math. 119 (1996), 109-128.
• [KMR] V. Kordula, V. Müller and V. Rakočević, On the semi-Browder spectrum, Studia Math. 123 (1997), 1-13.
• [MM] M. Mbekhta and V. Müller, On the axiomatic theory of spectrum II, ibid. 119 (1996), 129-147.
• [MW] A. M. Meléndez and A. Wawrzyńczyk, An approach to joint spectra, Ann. Polon. Math. 72 (1999), 131-144.
• [O1] K. K. Oberai, On the Weyl spectrum, Illinois J. Math. 18 (1974), 208-212.
• [O2] K. K. Oberai, Spectral mapping theorem for essential spectra, Rev. Roumaine Math. Pures Appl. 25 (1980), 365-373.
• [R1] V. Rakočević, Approximate point spectrum and commuting compact perturbations, Glasgow Math. J. 28 (1986), 193-198.
• [R2] V. Rakočević, On the essential spectrum, Zb. Rad. 6 (1992), 39-48.
• [S] M. Schechter, On the essential spectrum of an arbitrary operator, J. Math. Anal. Appl. 13 (1966), 205-215.
• [Z1] J. Zemánek, Compressions and the Weyl-Browder spectra, Proc. Roy. Irish Acad. Sect. A 86 (1986), 57-62.
• [Z2] J. Zemánek, Approximation of the Weyl spectrum, ibid. 87 (1987), 177-180.