Weak-operator Continuity and the Existence of Adjoints

1999 ◽  
Vol 45 (2) ◽  
pp. 203-206 ◽  
Author(s):  
Douglas Bridges ◽  
Luminita Dediu
Keyword(s):  
Weak Operator

Some properties of D-weak operator topology

2020 ◽  
Vol 70 (3) ◽  
pp. 753-758
Author(s):  
Marcel Polakovič
Keyword(s):  
Hilbert Space ◽  
Effect Algebra ◽  
Linear Subspace ◽  
Linear Operators ◽  
Positive Linear Operators ◽  
Weak Operator Topology ◽  
Generalized Effect Algebra ◽  
Weak Operator ◽  
Dense Linear Subspace

AbstractLet 𝓖D(𝓗) denote the generalized effect algebra consisting of all positive linear operators defined on a dense linear subspace D of a Hilbert space 𝓗. The D-weak operator topology (introduced by other authors) on 𝓖D(𝓗) is investigated. The corresponding closure of the set of bounded elements of 𝓖D(𝓗) is the whole 𝓖D(𝓗). The closure of the set of all unbounded elements of 𝓖D(𝓗) is also the set 𝓖D(𝓗). If Q is arbitrary unbounded element of 𝓖D(𝓗), it determines an interval in 𝓖D(𝓗), consisting of all operators between 0 and Q (with the usual ordering of operators). If we take the set of all bounded elements of this interval, the closure of this set (in the D-weak operator topology) is just the original interval. Similarly, the corresponding closure of the set of all unbounded elements of the interval will again be the considered interval.

scholarly journals Some Fixed Point Theory Results for the Interpolative Berinde Weak Operator

2020 ◽  
pp. 253-271 ◽  
Author(s):  
Clement Boateng Ampadu
Keyword(s):  
Metric Spaces ◽  
Fixed Point Theory ◽  
Existence Theorems ◽  
Point Theory ◽  
Picard Iteration ◽  
Partial Metric ◽  
Weak Contraction ◽  
Nonlinear Anal ◽  
Partial Metric Spaces ◽  
Weak Operator

Partially inspired by [Erdal Karapinar, Ravi Agarwal and Hassen Aydi, Interpolative Reich-Rus-Ćirić type contractions on partial metric spaces, Mathematics 6 (2018), 256] and [V. Berinde, Approximating fixed points of weak contractions using the Picard iteration, Nonlinear Anal. Forum 9(1) (2004), 43-53], we introduce a concept of interpolative Berinde weak contraction, and obtain some existence theorems for mappings satisfying such a contractive definition, and some of its extensions.

A note on weak operator precedence grammars

1978 ◽  
Vol 7 (5) ◽  
pp. 213-218
Author(s):  
I.H. Sudborough
Keyword(s):  
Weak Operator

On Weak Operator Compactness of the Unit Ball ofL(H)

1978 ◽  
Vol 24 (31-36) ◽  
pp. 493-494 ◽  
Author(s):  
Douglas S. Bridges
Keyword(s):  
Unit Ball ◽  
Weak Operator

scholarly journals G -convergence and the weak operator topology

PAMM ◽  
2016 ◽  
Vol 16 (1) ◽  
pp. 883-884 ◽  
Author(s):  
Marcus Waurick
Keyword(s):  
Weak Operator Topology ◽  
Weak Operator

A representation theorem for a complete Boolean algebra of projections

1979 ◽  
Vol 83 (3-4) ◽  
pp. 225-237 ◽  
Author(s):  
H. R. Dowson ◽  
T. A. Gillespie
Keyword(s):  
Banach Space ◽  
Hilbert Space ◽  
Boolean Algebra ◽  
Complex Banach Space ◽  
Complex Hilbert Space ◽  
Complete Boolean Algebra ◽  
Norm Topology ◽  
Weak Operator ◽  
Bounded Sets ◽  
Algebra Of Operators

SynopsisLet B be a complete Boolean algebra of projections on a complex Banach space X and let (B) denote the closed algebra of operators generated by B in the norm topology. It is shown that there is a complex Hilbert space H, a complete Boolean algebra B0 of self-adjoint projections on H, and an algebraic isomorphism of B onto B. This isomorphism is bicontinuous when B and B are endowed with the norm topologies, the weak operator topologies or the ultraweak operator topologies. It is also bicontinuous on bounded sets with respect to the strong operator topologies on B and B. As an application, it is shown that the weak and ultraweak operator topologies in fact coincide on B.

scholarly journals NEW INSIGHTS CONCERNING DIMENSION EIGHT EFFECTS IN WEAK DECAYS

2001 ◽  
Vol 16 (supp01c) ◽  
pp. 1228-1230
Author(s):  
JOHN F. DONOGHUE
Keyword(s):  
Operator Product Expansion ◽  
Short Distance ◽  
Numerical Estimate ◽  
Dimensional Regularization ◽  
Operator Product ◽  
Higher Dimension ◽  
Matrix Elements ◽  
Weak Decays ◽  
The Matrix ◽  
Weak Operator

Most past work on weak nonleptonic decays has mixed dimensional regularization in the weak operator product expansion with some form of a cutoff regularization in the evaluation of the matrix elements. Even with the usual technique of matching the two schemes, this combination misses physics at short distance which can be described by dimension eight (and higher dimension) operators. I describe some recent work with V. Cirigliano and E. Golowich which clarifies these effects and provides a numerical estimate suggesting that they are important.

scholarly journals On the algebra generated by a Hermitian operator

1972 ◽  
Vol 18 (2) ◽  
pp. 89-91 ◽  
Author(s):  
H. R. Dowson
Keyword(s):  
Linear Operator ◽  
Bounded Linear Operator ◽  
Hermitian Operator ◽  
Bounded Linear ◽  
Weak Operator Topology ◽  
Weak Operator

The purpose of this note is to solve a problem of Dr A. M. Sinclair. Denote by Aw(I, T) the algebra with identity generated by a bounded linear operator T in the weak operator topology. We prove the following result.

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