Local spectral theory of endomorphisms of the disk algebra

• Autorzy: Trivedi S. , Chandra H.
• Języki publikacji: EN

Abstrakty

EN

Let A(D) denote the disk algebra. Every endomorphism of A(D) is induced by some φ (…) A(D) with ║φ║ ≤ 1. In this paper, it is shown that if φ is not an automorphism of D and φ has a fixed point in the open unit disk then the endomorphism induced by φ is decomposable if and only if the fixed set of φ is singleton. Further, we determine the local spectra of the endomorphism induced by φ in the cases when the fixed set of φ either includes unit circle or is a singleton.

Słowa kluczowe

EN

composition operator; decomposability and super-decomposability; endomorphism; local spectrum; Single Valued Extension Property

PL

operator złożony; endomorfizm

• Wydawca: De Gruyter
• Czasopismo: Demonstratio Mathematica
• Rocznik: 2016
• Tom: Vol. 49, nr 1
• Strony: 95--106
• Opis fizyczny: Bibliogr. 14 poz.

Twórcy

autor

Trivedi S.

• Department of Mathematics and Dst-Cims Banaras Hindu University Varanasi, India-221005

autor

Chandra H.

• Department of Mathematics and Dst-Cims Banaras Hindu University Varanasi, India-221005

Bibliografia

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• [10] M. Mbekhta, Sur la théorie spectrale locale et limite des nilpotents, Proc. Amer. Math. Soc. 110 (1990), 621–631.
• [11] T. L. Miller, V. G. Miller, An operator satisfying Dunford’s condition (C) but without Bishop’s property (β), Glasgow Math. J. 40 (1998), 427–430.
• [12] C. Schmoeger, Semi-Fredholm operators and local spectral theory, Demonstratio Math.4 (1995), 997–1004.
• [13] S. Trivedi, H. Chandra, Some results on local spectral theory of composition operators on lp spaces, Mat. Vesnik 66 (2014), 294–300.
• [14] P. Vrbová, On local spectral properties of operators in Banach spaces, Czechoslovak Math. J. 23(98) (1973), 483–492.

Uwagi

PL

Opracowanie ze środków MNiSW w ramach umowy 812/P-DUN/2016 na działalność upowszechniającą naukę.