scholarly journals On strictly quasi-Fredholm linear relations and semi-B-Fredholm linear relation perturbations

Filomat ◽  
2017 ◽  
Vol 31 (20) ◽  
pp. 6337-6355 ◽  
Author(s):  
Bouaniza Hafsa ◽  
Maher Mnif
Keyword(s):  
Finite Rank ◽  
Linear Relation ◽  
Linear Relations ◽  
Finite Rank Operators ◽  
Lower Semi ◽  
The Stability

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.

Left-right fredholm and left-right browder linear relations

Filomat ◽  
2017 ◽  
Vol 31 (2) ◽  
pp. 255-271 ◽  
Author(s):  
T. Álvarez ◽  
Fatma Fakhfakh ◽  
Maher Mnif
Keyword(s):  
Banach Space ◽  
Finite Rank ◽  
Linear Relation ◽  
Finite Rank Operator ◽  
Linear Relations ◽  
Rank Operator ◽  
Type Decomposition ◽  
Converse Results

In this paper we introduce the notions of left (resp. right) Fredholm and left (resp. right) Browder linear relations. We construct a Kato-type decomposition of such linear relations. The results are then applied to give another decomposition of a left (resp. right) Browder linear relation T in a Banach space as an operator-like sum T = A + B, where A is an injective left (resp. a surjective right) Fredholm linear relation and B is a bounded finite rank operator with certain properties of commutativity. The converse results remain valid with certain conditions of commutativity. As a consequence, we infer the characterization of left (resp. right) Browder spectrum under finite rank operator.

scholarly journals A new variation of Weyl type theorems and perturbations

Filomat ◽  
2014 ◽  
Vol 28 (9) ◽  
pp. 1899-1906 ◽  
Author(s):  
Junli Shen ◽  
Alatancang Chen
Keyword(s):  
Finite Rank ◽  
Necessary Conditions ◽  
Finite Rank Operators ◽  
Weyl Type Theorems ◽  
Nilpotent Operators ◽  
Sufficient And Necessary Conditions ◽  
The Stability ◽  
Algebraic Operators

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.

PROPERTY (Bgw) AND PERTURBATIONS

2014 ◽  
Vol 0 (0) ◽  
Author(s):  
M.H.M. Rashid ◽  
T. Prasad
Keyword(s):  
Banach Space ◽  
Finite Rank ◽  
Point Spectrum ◽  
Space Operator ◽  
Approximate Point Spectrum ◽  
Finite Rank Operators ◽  
Riesz Operators ◽  
Nilpotent Operators ◽  
The Stability ◽  
Isolated Eigenvalues

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.

scholarly journals Approximation by finite rank operators

1981 ◽  
Vol 33 (3) ◽  
pp. 199-213 ◽  
Author(s):  
Frank Deutsch ◽  
Jaroslav Mach ◽  
Klaus Saatkamp
Keyword(s):  
Finite Rank ◽  
Finite Rank Operators

Range Inclusion for Multilinear Mappings: Applications

1985 ◽  
Vol 28 (3) ◽  
pp. 317-320
Author(s):  
C. K. Fong
Keyword(s):  
Hilbert Space ◽  
Finite Rank ◽  
Trace Class ◽  
Inner Derivation ◽  
Finite Rank Operators ◽  
Multilinear Mappings ◽  
Trace Class Operators ◽  
The Ideal

AbstractThe result of S. Grabiner [5] on range inclusion is applied for establishing the following two theorems: 1. For A, B ∊ L(H), two operators on the Hilbert space H, we have DBC0(H) ⊆ DAL(H) if and only if DBC1(H) ⊆ DAL(H), where DA is the inner derivation which sends S ∊ L(H) to AS - SA, C1(H) is the ideal of trace class operators and C0(H) is the ideal of finite rank operators. 2. (Due to Fialkow [3]) For A, B ∊ L(H), we write T(A, B) for the map on L(H) sending S to AS - SB. Then the range of T(A, B)is the whole L(H) if it includes all finite rank operators L(H).

scholarly journals Quantities related to upper and lower semi-Fredholm type linear relations

2002 ◽  
Vol 66 (2) ◽  
pp. 275-289 ◽  
Author(s):  
Teresa Alvarez ◽  
Ronald Cross ◽  
Diane Wilcox
Keyword(s):  
Perturbation Theory ◽  
General Setting ◽  
Linear Operators ◽  
Normed Spaces ◽  
Fredholm Type ◽  
Linear Relations ◽  
Lower Semi ◽  
Strictly Singular

Certain norm related functions of linear operators are considered in the very general setting of linear relations in normed spaces. These are shown to be closely related to the theory of strictly singular, strictly cosingular, F+ and F− linear relations. Applications to perturbation theory follow.

scholarly journals Spatial Numerical Range of Operators on Weighted Hardy Spaces

2011 ◽  
Vol 2011 ◽  
pp. 1-8 ◽  
Author(s):  
Abdolaziz Abdollahi ◽  
Mohammad Taghi Heydari
Keyword(s):  
Hardy Spaces ◽  
Finite Rank ◽  
Numerical Range ◽  
Compact Operators ◽  
Weighted Hardy Spaces ◽  
Finite Rank Operators

We consider the spatial numerical range of operators on weighted Hardy spaces and give conditions for closedness of numerical range of compact operators. We also prove that the spatial numerical range of finite rank operators on weighted Hardy spaces is star shaped; though, in general, it does not need to be convex.

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