Hermitian and algebraic $^*$-algebras, representable extensions of positive functionals

2021 ◽  
Vol 256 (3) ◽  
pp. 311-343
Author(s):  
Zsolt Szűcs ◽  
Balázs Takács
Keyword(s):  
Positive Functionals

scholarly journals Positive functionals and oscillation criteria for second order differential systems

1979 ◽  
Vol 22 (3) ◽  
pp. 277-290 ◽  
Author(s):  
Garret J. Etgen ◽  
Roger T. Lewis
Keyword(s):  
Differential Equation ◽  
Hilbert Space ◽  
Second Order ◽  
Linear Operators ◽  
The Self ◽  
Differential Systems ◽  
Bounded Linear ◽  
Positive Functionals ◽  
Image Position ◽  
Adjoint Operators

Let ℋ be a Hilbert space, let ℬ = (ℋ, ℋ) be the B*-algebra of bounded linear operators from ℋ to ℋ with the uniform operator topology, and let ℒ be the subset of ℬ consisting of the self-adjoint operators. This article is concerned with the second order self-adjoint differential equation

scholarly journals Hermite-Fejér type interpolation and Korovkin's theorem

1990 ◽  
Vol 42 (3) ◽  
pp. 383-390
Author(s):  
H.-B. Knoop ◽  
F. Locher
Keyword(s):  
Uniform Convergence ◽  
Jacobi Polynomials ◽  
Korovkin Theorem ◽  
Type Interpolation ◽  
Special Values ◽  
Convergence Results ◽  
Interpolation Operators ◽  
Positive Functionals ◽  
Interpolation Polynomials ◽  
Korovkin’S Theorem

In this note we consider Hermite-Fejér interpolation at the zeros of Jacobi polynomials and with additional boundary conditions. For the associated Hermite-Fejér type operators and special values of α, β it was proved by the first author in recent papers that one has uniform convergence on the whole interval [−1,1]. The second author could show by introducing the concept of asymptotic positivity how to get the known convergence results for the classical Hermite-Fejér interpolation operators. In the present paper we show, using a slightly modified Bohman-Korovkin theorem for asymptotically positive functionals, that the Hermite-Fejér type interpolation polynomials , converge pointwise to f for arbitrary α, β > −1. The convergence is uniform on [−1 + δ,1 − δ].

Positive functionals on BP*-algebras

1977 ◽  
Vol 8 (1) ◽  
pp. 15-28 ◽  
Author(s):  
T. Husain ◽  
S. A. Warsi
Keyword(s):  
Positive Functionals
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