finite rank operators
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2020 ◽  
Vol 6 (1) ◽  
Author(s):  
R. Eskandari ◽  
F. Mirzapour

2020 ◽  
Vol 2020 ◽  
pp. 1-11 ◽  
Author(s):  
Awad A. Bakery ◽  
Afaf R. Abou Elmatty

Let E be a weighted Nakano sequence space or generalized Cesáro sequence space defined by weighted mean and by using s−numbers of operators from a Banach space X into a Banach space Y. We give the sufficient (not necessary) conditions on E such that the components SEX,Y≔T∈LX,Y:snTn=0∞∈E of the class SE form pre-quasi operator ideal, the class of all finite rank operators are dense in the Banach pre-quasi ideal SE, the pre-quasi operator ideal formed by the sequence of approximation numbers is strictly contained for different weights and powers, the pre-quasi Banach Operator ideal formed by the sequence of approximation numbers is small, and finally, the pre-quasi Banach operator ideal constructed by s−numbers is simple Banach space.


2017 ◽  
Vol 273 (9) ◽  
pp. 2815-2845 ◽  
Author(s):  
Xuanhao Ding ◽  
Yueshi Qin ◽  
Dechao Zheng

Filomat ◽  
2017 ◽  
Vol 31 (20) ◽  
pp. 6337-6355 ◽  
Author(s):  
Bouaniza Hafsa ◽  
Maher Mnif

In this paper we introduce the set of strictly quasi-Fredholm linear relations and we give some of its properties. Furthermore, we study the connection between this set and some classes of linear relations related to the notions of ascent, essentially ascent, descent and essentially descent. The obtained results are used to study the stability of upper semi-B-Fredholm and lower semi-B-Fredholm linear relations under perturbation by finite rank operators.


2016 ◽  
Vol 2016 ◽  
pp. 1-6
Author(s):  
Awad A. Bakery

We give sufficient conditions on a special space of sequences defined by Mohamed and Bakery (2013) such that the finite rank operators are dense in the complete space of operators whose approximation numbers belong to this sequence space. Hence, under a few conditions, every compact operator would be approximated by finite rank operators. We apply it on the sequence space defined by Tripathy and Mahanta (2003). Our results match those known forp-absolutely summable sequences of reals.


Author(s):  
M.H.M. Rashid ◽  
T. Prasad

AbstractA Banach space operator T satisfies property (Bgw) if the complement in the approximate point spectrum σa(T) of the semi-B-essential approximate point spectrum σSHF+-(T) coincides with the set of isolated eigenvalues of T of Unite multiplicity E°(T). We find conditions for Banach Space operator tosatfafy the property (Bgw). We also study the stability of property (Bgw) under perturbations by nilpotent operators, by finite rank operators, by quasi-nilpotent operators and by Riesz operators commuting with T.


Author(s):  
Kamila Kliś-Garlicka

AbstractIt was shown that the space of Toeplitz operators perturbated by finite rank operators is 2-hyperreflexive.


2014 ◽  
Vol 04 (09) ◽  
pp. 499-505
Author(s):  
J. C. Cabello ◽  
R. Casas ◽  
P. Montiel

Filomat ◽  
2014 ◽  
Vol 28 (9) ◽  
pp. 1899-1906 ◽  
Author(s):  
Junli Shen ◽  
Alatancang Chen

In this paper, we introduce the new property (aR), which extends property (R) introduced by Aiena and his collaborators. We investigate the property (aR) in connection with Weyl type theorems, and establish sufficient and necessary conditions for which property (aR) holds. We also study the stability of property (aR) under perturbations by finite rank operators, by nilpotent operators, by quasi-nilpotent operators and by algebraic operators commuting with T.


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