scholarly journals Characterising dominated weak-operator continuous functionals on subspaces ofB(H)

2013 ◽  
Vol 164 (4) ◽  
pp. 416-420
Author(s):  
Douglas S. Bridges
Keyword(s):  
Weak Operator ◽  
Continuous Functionals

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.

R.E. degrees of continuous functionals

1983 ◽  
Vol 23 (1) ◽  
pp. 79-98 ◽  
Author(s):  
Dag Normann
Keyword(s):  
Continuous Functionals

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

scholarly journals Some hemivariational inequalities in the Euclidean space

2019 ◽  
Vol 9 (1) ◽  
pp. 958-977 ◽  
Author(s):  
Giovanni Molica Bisci ◽  
Dušan Repovš
Keyword(s):  
Weak Solution ◽  
Euclidean Space ◽  
Sobolev Space ◽  
Hemivariational Inequalities ◽  
Existence Of Weak Solutions ◽  
Lipschitz Continuous ◽  
Variational Structure ◽  
Locally Lipschitz ◽  
Sign Changing Solutions ◽  
Continuous Functionals

Abstract The purpose of this paper is to study the existence of weak solutions for some classes of hemivariational problems in the Euclidean space ℝd (d ≥ 3). These hemivariational inequalities have a variational structure and, thanks to this, we are able to find a non-trivial weak solution for them by using variational methods and a non-smooth version of the Palais principle of symmetric criticality for locally Lipschitz continuous functionals, due to Krawcewicz and Marzantowicz. The main tools in our approach are based on appropriate theoretical arguments on suitable subgroups of the orthogonal group O(d) and their actions on the Sobolev space H1(ℝd). Moreover, under an additional hypotheses on the dimension d and in the presence of symmetry on the nonlinear datum, the existence of multiple pairs of sign-changing solutions with different symmetries structure has been proved. In connection to classical Schrödinger equations a concrete and meaningful example of an application is presented.

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