Some properties of D-weak operator topology
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Marcel Polakovič
Abstract
Let 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.
Communicated by Mirko Navara
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- Regular papers
- Recurrences for the genus polynomials of linear sequences of graphs
- The existence of states on EQ-algebras
- On sidon sequences of farey sequences, square roots and reciprocals
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- Refinement of fejér inequality for convex and co-ordinated convex functions
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- Coefficients problems for families of holomorphic functions related to hyperbola
- Triebel-Lizorkin capacity and hausdorff measure in metric spaces
- The method of upper and lower solutions for integral boundary value problem of semilinear fractional differential equations with non-instantaneous impulses
- On a system of three difference equations of higher order solved in terms of Lucas and Fibonacci numbers
- Density of summable subsequences of a sequence and its applications
- Rough weighted 𝓘-limit points and weighted 𝓘-cluster points in θ-metric space
- A note on cosine series with coefficients of generalized bounded variation
- Some geometric properties of the non-Newtonian sequence spaces lp(N)
- On sequence spaces defined by the domain of a regular tribonacci matrix
- Jointly separating maps between vector-valued function spaces
- Some fixed point theorems for multi-valued mappings in graphical metric spaces
- Monotone transformations on the cone of all positive semidefinite real matrices
- Locally defined operators in the space of Ck,ω-functions
- Some properties of D-weak operator topology
- Estimating the distribution of a stochastic sum of IID random variables
- An internal characterization of complete regularity
