scholarly journals On the norm of symmetrised two-sided multiplications

2003 ◽  
Vol 67 (1) ◽  
pp. 27-38 ◽  
Author(s):  
Bojan Magajna ◽  
Aleksej Turnšek
Keyword(s):  
Lower Bounds ◽  
Linear Operators ◽  
Bounded Norm

The authors provide precise lower bounds for the completely bounded norm of the operator Ta,b: ß(H) → ß(H) defined by Ta,b (x) = axb + bxa and the injective norm of the corresponding tensor. Further, they compute the norm of the operator x ↦ a*xb + b*xa acting on the space of all conjugate-linear operators on H.

Lower bounds for the spectrum of a second order linear differential equation with a coefficient whose negative part is p-integrable

1984 ◽  
Vol 97 ◽  
pp. 105-107
Author(s):  
B. J. Harris
Keyword(s):  
Differential Equation ◽  
Boundary Conditions ◽  
Linear Differential Equation ◽  
Differential Expression ◽  
Lower Bounds ◽  
Linear Operators ◽  
Order Linear Differential Equation ◽  
Negative Part ◽  
Order Linear ◽  
Linear Differential

SynopsisWe consider ihe differential expression M[y]: = −y″ + qy on [0, ∞) where q_∈ Lp [0, ∞) for some p ≧ 1. It is known that M, together with the boundary conditions y(0) = 0 or y′(0) = 0, defines linear operators on L2 [0, ∞). We obtain lower bounds for the spectra of these operators. Our bounds depend on the Lp norm of q_ and extend results of Everitt and Veling.

scholarly journals Lower bounds for some factorable matrices

2006 ◽  
Vol 2006 ◽  
pp. 1-13 ◽  
Author(s):  
B. E. Rhoades ◽  
Pali Sen
Keyword(s):  
Lower Bounds ◽  
Linear Operators ◽  
Bounded Linear Operators ◽  
Bounded Linear ◽  
Factorable Matrices

We determine the lower bounds for classes of Rhaly matrices, considered as bounded linear operators onℓp. We improve on and provide correct proofs of the results of the first author (1990).

9.—Bivariational Bounds associated with Non-self-adjoint Linear Operators

1976 ◽  
Vol 75 (2) ◽  
pp. 109-118 ◽  
Author(s):  
Michael F. Barnsley ◽  
Peter D. Robinson
Keyword(s):  
Hilbert Space ◽  
Lower Bounds ◽  
Positive Constant ◽  
Real Hilbert Space ◽  
Linear Operators ◽  
Time Dependent ◽  
Diffusion Equations ◽  
Inner Product ◽  
Upper And Lower Bounds ◽  
Fredholm Integral Equations

SYNOPSISLet A be a closed linear transformation from a real Hilbert space ℋ, with symmetric inner product 〈, 〉, into itself; and let f ∈ ℋ be given such that the problem Aø = f has a solution ø ∈ D(A), the domain of A. Then bivariational upper and lower bounds on 〈g, ø〉 for any g ∈ ℋ are exhibited when there exists a positive constant a such that 〈AΦ, AΦ⊖ ≧ a2〈Φ, Φ〉 for all Φ ∈ D(A). The applicability of the theory both to Fredholm integral equations and also to time-dependent diffusion equations is demonstrated.

Approximation in statistical sense to B -continuous functions by positive linear operators

2010 ◽  
Vol 47 (3) ◽  
pp. 289-298 ◽  
Author(s):  
Fadime Dirik ◽  
Oktay Duman ◽  
Kamil Demirci
Keyword(s):  
Compact Subset ◽  
Real Line ◽  
Statistical Convergence ◽  
Approximation Theorem ◽  
Continuous Functions ◽  
Linear Operators ◽  
Positive Linear Operators ◽  
Statistical Approximation ◽  
Classical Version ◽  
Statistical Sense

In the present work, using the concept of A -statistical convergence for double real sequences, we obtain a statistical approximation theorem for sequences of positive linear operators defined on the space of all real valued B -continuous functions on a compact subset of the real line. Furthermore, we display an application which shows that our new result is stronger than its classical version.

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