Tensor product and property (b). (English) Zbl 1399.47070
Summary: 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.
Reviewer: Arne Winterhof (Linz)
MSC:
| 47A80 | Tensor products of linear operators |
| 47A55 | Perturbation theory of linear operators |
| 47A53 | (Semi-) Fredholm operators; index theories |
| 47B20 | Subnormal operators, hyponormal operators, etc. |
References:
| [1] | P. Aiena, Fredholm and Local Spectral Theory, with Applications to Multipliers (Kluwer Academic Publishers, Dordrecht, 2004) · Zbl 1077.47001 |
| [2] | P. Aiena, J. Guil · Zbl 1136.47003 · doi:10.1016/j.laa.2007.10.022 |
| [3] | P. Aiena, M.T. Biondi, · Zbl 1171.47011 · doi:10.1016/j.jmaa.2008.11.081 |
| [4] | M. Berkani, H. Zariouh, Extended Weyl type theorems. Math. Bohemica 134(4), 369–378 (2009) · Zbl 1211.47011 |
| [5] | M. Berkani, M. Sarih, H. Zariouh, Browder-type theorems and SVEP. Mediterr. J. Math. 6, 139–150 (2010) · Zbl 1241.47008 |
| [6] | A. Brown, C. Pearcy, Spectra of tensor products of operators. Proc. Am. Math. Soc. 17, 162–166 (1966) · Zbl 0141.32202 · doi:10.1090/S0002-9939-1966-0188786-5 |
| [7] | B.P. Duggal, Hereditarily normaloid operators. Extr. Math. 20, 203–217 (2005) · Zbl 1097.47005 |
| [8] | B.P. Duggal, S.V. Djordjevi\`c, C.S. Kubrus · Zbl 1241.47016 · doi:10.1007/s12215-010-0035-x |
| [9] | B.P. Duggal, Ten · Zbl 1231.47016 · doi:10.1007/s12215-011-0023-9 |
| [10] | C.S. Kubrusly, B.P. Duggal, On Weyl and Browder spectra of tensor product. Glasgow Math. J. 50, 289–302 (2008) · Zbl 1136.47013 · doi:10.1017/S0017089508004205 |
| [11] | B.P. Duggal, R. Harte, A.H. Kim, Weyl’s theorem, tensor products and multiplication operators II. Glasgow Math. J. 52, 705–709 (2010) · Zbl 1197.47050 · doi:10.1017/S0017089510000522 |
| [12] | M. Oudghiri, a-Weyl’s theorem and perturbations. Stud. Math. 173, 193–201 (2006) · Zbl 1097.47013 · doi:10.4064/sm173-2-6 |
| [13] | V. Rakocevi\`c, On a class of operators. Math. Vesnik. 37, 423–426 (1985) |
| [14] | M. Schechter, R. Whitley, Best Fredholm perturbation theorems. Stud. Math. 90, 175–190 (1988) · Zbl 0611.47010 · doi:10.4064/sm-90-3-175-190 |
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.
