×

Perturbation of semi-Browder linear relations by commuting Riesz operators. (English) Zbl 1502.47002

Summary: This paper is devoted to the investigation of the stability of upper semi-Browder, lower semi-Browder and Browder linear relations which satisfy the stabilization property, under commuting Riesz operator perturbations. As applications, we infer the invariance of the corresponding Browder’s essential approximate point spectrum, Browder’s essential defect spectrum and Browder’s essential spectrum under commuting Riesz operator perturbations.

MSC:

47A06 Linear relations (multivalued linear operators)
47A53 (Semi-) Fredholm operators; index theories
47A55 Perturbation theory of linear operators
47B06 Riesz operators; eigenvalue distributions; approximation numbers, \(s\)-numbers, Kolmogorov numbers, entropy numbers, etc. of operators
PDFBibTeX XMLCite
Full Text: DOI

References:

[1] Cross, R., Multivalued theorem for the product of linear relations, Linear Algebra and its Applications, 277, 127-134 (1998) · Zbl 0940.15002
[2] Grabiner, S., Ascent, descent and compact perturbations, Proc Am Math Soc, 71, 79-80 (1978) · Zbl 0392.47002
[3] Rakocevic, V., Semi-Fredholm operators with finite ascent or descent and perturbations, Proc Am Math Soc, 123, 3823-3825 (1995) · Zbl 0854.47008
[4] Rakocevic, V., Semi-Browder operators and perturbations, Stud Math, 122, 131-137 (1997) · Zbl 0892.47015
[5] Caradus, Sr; Pfaffenberger, We; Yood, B., Calkin algebras and algebras of operators on Banach spaces (1974), New York (NY): Marcel Dekker, New York (NY) · Zbl 0299.46062
[6] Fakhfakh, F.; Mnif, M., Perturbation of semi-Browder operators and stability of Browder’s essential defect and approximate point spectrum, J Math Anal Appl, 347, 235-242 (2008) · Zbl 1151.47020
[7] Fakhfakh, F.; Mnif, M., Browder and semi-Browder operators and perturbation function, J Extracta Math, 24, 219-241 (2009) · Zbl 1208.47020
[8] Rakocevic, V., Approximate point spectrum and commuting compact perturbations, Glasgow Math J, 28, 193-198 (1986) · Zbl 0602.47003
[9] Fakhfakh, F.; Mnif, M., Perturbation theory of lower semi-Browder multivalued linear operators, Publ Math Debrecen, 78, 595-606 (2011) · Zbl 1229.47006
[10] Alvarez, T.; Fakhfakh, F.; Mnif, M., Coperturbation function and lower semi-Browder multivalued linear operators, Linear Multilinear Algebra, 61, 494-516 (2013) · Zbl 1277.47004
[11] Wilcox, D., Multivalued semi-Fredholm operators in normed linear spaces, [doctoral thesis] (2002), University of Cape Town
[12] Sandovici, A., H. d. Snoo, H. Winkler, Ascent, descent, nullity, defect, and related notions for linear relations in linear spaces, Linear Algebra Appl, 423, 456-497 (2007) · Zbl 1124.47003
[13] Lambek, J., Lectures on rings and modules (1966), Massachusetts-Toronto-London, Blaisdell: Waltham, Massachusetts-Toronto-London, Blaisdell · Zbl 0143.26403
[14] Alvarez, T., On regular linear relations, Acta Math Sinica English Ser, 28, 183-194 (2012) · Zbl 1483.47005
[15] Chafai, E.; Mnif, M., Descent and essential descent spectrum of linear relations, Extracta Math, 29, 117-139 (2014) · Zbl 1347.47001
[16] Alvarez, T.; Wilcox, D., Perturbation theory of multivalued Atkinson operators in normed spaces, Bull Aust Math Soc, 76, 195-204 (2007) · Zbl 1145.47001
[17] Chafai, E., Ascent, Descent and some perturbation results for linear relations, [doctoral thesis] (2013), University of Sfax-Tunisie
[18] Chafai, E.; Mnif, M., Spectral mapping theorem for ascent, essential ascent, descent and essential descent spectrum of linear relations, Acta Math Sci, 34, 1212-1224 (2014) · Zbl 1324.47006
[19] Tylli, H-O, On the asymptotic behaviour of some quantities related to semi-Fredholm operators, J London Math Soc, 31, 340-348 (1985) · Zbl 0582.47004
[20] Chamkha, Y.; Mnif, M., Browder spectra of upper triangular matrix linear relations, Publ Math Debrecen, 82, 569-590 (2013) · Zbl 1289.47001
[21] Goldman, Ma; Kračkovskii, Sn, Behaviour of the space of zero elements with finite-dimensional salient on the Riesz kernel under perturbations of the operator, Dokl Akad Nauk SSSR, 221, 532-534 (1975)
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.