Abstract
A Banach space operator satisfies property (b) if the complement of its essential Weyl approximate point spectrum in its approximate point spectrum is the set of all poles of the resolvent of finite rank. Property (b) does not transfer from operators A and B to their tensor product \(A\otimes B;\) we give necessary and/or sufficient conditions ensuring the passage of property (b) from A and B to \(A\otimes B.\) Perturbations by Riesz operators are considered.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
P. Aiena, Fredholm and Local Spectral Theory, with Applications to Multipliers (Kluwer Academic Publishers, Dordrecht, 2004)
P. Aiena, J. Guillen, P. Peñna, Property \((w)\) for perturbations of polaroid operators. Linear Algebra Appl. 428, 1791–1802 (2008)
P. Aiena, M.T. Biondi, F. Villafañe, Property \((w)\) and perturbations III. J. Math. Anal. Appl. 353, 205–214 (2009)
M. Berkani, H. Zariouh, Extended Weyl type theorems. Math. Bohemica 134(4), 369–378 (2009)
M. Berkani, M. Sarih, H. Zariouh, Browder-type theorems and SVEP. Mediterr. J. Math. 6, 139–150 (2010)
A. Brown, C. Pearcy, Spectra of tensor products of operators. Proc. Am. Math. Soc. 17, 162–166 (1966)
B.P. Duggal, Hereditarily normaloid operators. Extr. Math. 20, 203–217 (2005)
B.P. Duggal, S.V. Djordjevic̀, C.S. Kubrusly, On the a-Browder and \(a\)-Weyl spectra of tensor products. Rend. Circ. Mat. Palermo 59, 473–481 (2010)
B.P. Duggal, Tensor product and property \((w)\). Rend. Circ. Mat. Palermo 60, 23 (2011). doi:10.1007/s12215-011-0023-9
C.S. Kubrusly, B.P. Duggal, On Weyl and Browder spectra of tensor product. Glasgow Math. J. 50, 289–302 (2008)
B.P. Duggal, R. Harte, A.H. Kim, Weyl’s theorem, tensor products and multiplication operators II. Glasgow Math. J. 52, 705–709 (2010)
M. Oudghiri, a-Weyl’s theorem and perturbations. Stud. Math. 173, 193–201 (2006)
V. Rakocevic̀, On a class of operators. Math. Vesnik. 37, 423–426 (1985)
M. Schechter, R. Whitley, Best Fredholm perturbation theorems. Stud. Math. 90, 175–190 (1988)
Acknowledgements
We thank the referee for his valuable suggestions that contributed greatly to this paper.
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Rashid, M.H.M. Tensor product and property (b). Period Math Hung 75, 376–386 (2017). https://doi.org/10.1007/s10998-017-0207-y
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10998-017-0207-y