scholarly journals Shift commutator algebras and multipliers

Filomat ◽  
2018 ◽  
Vol 32 (17) ◽  
pp. 5837-5843
Author(s):  
A.L. Barrenechea
Keyword(s):  
Hilbert Space ◽  
Shift Operator ◽  
Commutator Algebra

We determine the precise structure of all multipliers on the commutator algebra associated to the shift operator on a Hilbert space. The problem has its own interest by its connection with the theory of Toeplitz and Laurent operators.

scholarly journals On Fuzzy Soft Linear Operators in Fuzzy Soft Hilbert Spaces

2020 ◽  
Vol 2020 ◽  
pp. 1-13
Author(s):  
Nashat Faried ◽  
Mohamed S. S. Ali ◽  
Hanan H. Sakr
Keyword(s):  
Hilbert Space ◽  
Hilbert Spaces ◽  
Shift Operator ◽  
Point Spectrum ◽  
Soft Set ◽  
Linear Operators ◽  
Comparison Spectrum ◽  
Left Shift ◽  
Definition Of ◽  
Soft Point

Due to the difficulty of representing problem parameters fuzziness using the soft set theory, the fuzzy soft set is regarded to be more general and flexible than using the soft set. In this paper, we define the fuzzy soft linear operator T~ in the fuzzy soft Hilbert space H~ based on the definition of the fuzzy soft inner product space U~,·,·~ in terms of the fuzzy soft vector v~fGe modified in our work. Moreover, it is shown that ℂnA, ℝnA and ℓ2A are suitable examples of fuzzy soft Hilbert spaces and also some related examples, properties and results of fuzzy soft linear operators are introduced with proofs. In addition, we present the definition of the fuzzy soft orthogonal family and the fuzzy soft orthonormal family and introduce examples satisfying them. Furthermore, the fuzzy soft resolvent set, the fuzzy soft spectral radius, the fuzzy soft spectrum with its different types of fuzzy soft linear operators and the relations between those types are introduced. Moreover, the fuzzy soft right shift operator and the fuzzy soft left shift operator are defined with an example of each type on ℓ2A. In addition, it is proved, on ℓ2A, that the fuzzy soft point spectrum of fuzzy soft right shift operator has no fuzzy soft eigenvalues, the fuzzy soft residual spectrum of fuzzy soft right shift operator is equal to the fuzzy soft comparison spectrum of it and the fuzzy soft point spectrum of fuzzy soft left shift operator is the fuzzy soft open disk λ~<~1~. Finally, it is shown that the fuzzy soft Hilbert space is fuzzy soft self-dual in this generalized setting.

scholarly journals On unilateral shift operators and C0-operators

1992 ◽  
Vol 53 (1) ◽  
pp. 137-142
Author(s):  
Il Bong Jung ◽  
Yong Chan Kim
Keyword(s):  
Hilbert Space ◽  
Shift Operator ◽  
Matrix Form ◽  
Operator Matrix ◽  
Unilateral Shift ◽  
Shift Operators

AbstractLet S(n) be a unilateral shift operator on a Hilbert space of multiplicity n. In this paper, we prove a generalization of the theorem that if S(1) is unitarily equivalent to an operator matrix form relative to a decomposition ℳ ⊕ N, then E is in a certain class C0 which will be defined below.

scholarly journals Dissipative operators and series inequalities

1981 ◽  
Vol 23 (3) ◽  
pp. 429-442 ◽  
Author(s):  
Herbert A. Gindler ◽  
Jerome A. Goldstein
Keyword(s):  
Hilbert Space ◽  
Sequence Space ◽  
Shift Operator ◽  
Contraction Semigroup ◽  
Best Constant ◽  
Dissipative Operators ◽  
Extremal Vectors

Of concern is the best constant K in the inequality ‖Ax‖2 ≤ K‖A2x‖‖x‖ where A generates a strongly continuous contraction semigroup in a Hilbert space. Criteria are obtained for approximate extremal vectors x when K = 2 (K ≤ 2 always holds). By specializing A + I to be a shift operator on a sequence space, very simple proofs of Copson's recent results on series inequalities follow. Inequalities of the above type are also studied on LP spaces, and earlier results of the authors and of Holbrook are improved.

Hilbert Space

1993 ◽  
Author(s):  
J. R. Retherford
Keyword(s):  
Hilbert Space
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