scholarly journals New Inequalities of Weaving K-Frames in Subspaces

Mathematics ◽  
2019 ◽  
Vol 7 (9) ◽  
pp. 863
Author(s):  
Zhong-Qi Xiang
Keyword(s):  
Linear Operators ◽  
Complex Numbers ◽  
Bounded Linear Operators ◽  
Bounded Linear ◽  
Double Inequality ◽  
Bounded Complex ◽  
New Inequalities

In the present paper, we obtain some new inequalities for weaving K-frames in subspaces based on the operator methods. The inequalities are associated with a sequence of bounded complex numbers and a parameter λ ∈ R . We also give a double inequality for weaving K-frames with the help of two bounded linear operators induced by K-dual. Facts prove that our results cover those recently obtained on weaving frames due to Li and Leng, and Xiang.

Representations and Divisibility of Operator Polynomials

1978 ◽  
Vol 30 (5) ◽  
pp. 1045-1069 ◽  
Author(s):  
I. Gohberg ◽  
P. Lancaster ◽  
L. Rodman
Keyword(s):  
Banach Space ◽  
Complex Banach Space ◽  
Linear Operators ◽  
Complex Numbers ◽  
Bounded Linear Operators ◽  
Bounded Linear ◽  
Image Position

Let be a complex Banach space and the algebra of bounded linear operators on . In this paper we study functions from the complex numbers to of the form

scholarly journals Norm of a linear combination of two operators on a Hilbert space

2002 ◽  
Vol 65 (1) ◽  
pp. 9-22
Author(s):  
Takahiko Nakazi ◽  
Takanori Yamamoto
Keyword(s):  
Hilbert Space ◽  
Linear Combination ◽  
Linear Operators ◽  
Operator Norm ◽  
Complex Numbers ◽  
Bounded Linear Operators ◽  
Bounded Linear

Let α, β γ, δ be complex numbers such that γδ ≠ 0. If A and B are bounded linear operators on the Hilbert space H such that γA + δB is right invertible then we study the operator norm of (αA + βB)(γA + δB)−1 using the angle φ between two subspaces ran A and ran B or the angle ψ = ψ(A, B) between two operators A and B where

On Certain Classes of Bounded Linear Operators

1970 ◽  
Vol 13 (4) ◽  
pp. 469-473
Author(s):  
C-S Lin
Keyword(s):  
Banach Space ◽  
Linear Operator ◽  
Banach Algebra ◽  
Fredholm Operator ◽  
Bounded Linear Operator ◽  
Complex Banach Space ◽  
Linear Operators ◽  
Complex Numbers ◽  
Bounded Linear Operators ◽  
Bounded Linear

Let T—c be a Fredholm operator, where T is a bounded linear operator on a complex Banach space and c is a scalar, the set of all such scalars is called the Φ-set of T [2] and was studied by many authors. In this connection, the purpose of the present paper is to investigate some classes Φ(V) of all such operators for any subset V of the complex plane.Let X be a Banach space over the field C of complex numbers with dim Z = ∞, unless otherwise stated, B(X) the Banach algebra of all bounded linear operators and K(X) the closed two-sided ideal of all compact operators on X.

scholarly journals Some inequalities for commutators of bounded linear operators in Hilbert spaces

Filomat ◽  
2011 ◽  
Vol 25 (2) ◽  
pp. 151-162 ◽  
Author(s):  
S.S. Dragomir
Keyword(s):  
Hilbert Spaces ◽  
Linear Operators ◽  
Bounded Linear Operators ◽  
Bounded Linear ◽  
New Inequalities

Some new inequalities for commutators that complement and in some instances improve recent results obtained by F. Kittaneh are given.

scholarly journals Further Inequalities for Sequences and Power Series of Operators in Hilbert Spaces Via Hermitian Forms

2016 ◽  
Vol 2 (1) ◽  
pp. 47-64
Author(s):  
S. S. Dragomir
Keyword(s):  
Power Series ◽  
Hilbert Spaces ◽  
Linear Operators ◽  
Bounded Linear Operators ◽  
Bounded Linear ◽  
Hermitian Forms ◽  
New Inequalities

Abstract By the use of some inequalities for nonnegative Hermitian forms some new inequalities for sequences and power series of bounded linear operators in complex Hilbert spaces are established. Applications for some fundamental functions of interest are also given.

Cline’s formula for g-Drazin inverses in a ring

Filomat ◽  
2019 ◽  
Vol 33 (8) ◽  
pp. 2249-2255
Author(s):  
Huanyin Chen ◽  
Marjan Abdolyousefi
Keyword(s):  
Operator Theory ◽  
Spectral Properties ◽  
Associative Ring ◽  
Linear Operators ◽  
Drazin Inverse ◽  
Bounded Linear Operators ◽  
Bounded Linear ◽  
Cline’S Formula

It is well known that for an associative ring R, if ab has g-Drazin inverse then ba has g-Drazin inverse. In this case, (ba)d = b((ab)d)2a. This formula is so-called Cline?s formula for g-Drazin inverse, which plays an elementary role in matrix and operator theory. In this paper, we generalize Cline?s formula to the wider case. In particular, as applications, we obtain new common spectral properties of bounded linear operators.

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