Let R be a linear subset of the space B(H) of bounded operators on a Hilbert space H with an orthonormal basis. It is shown constructively that if the unit ball of R is weak-operator totally bounded, then an ultraweakly continuous linear functional on R extends to one on B(H), and the extended funct
Absolutely Convergent Extensions of Nonclosable Positive Linear Functionals
✍ Scribed by Giorgia Bellomonte; Camillo Trapani; Salvatore Triolo
- Publisher
- SP Birkhäuser Verlag Basel
- Year
- 2010
- Tongue
- English
- Weight
- 241 KB
- Volume
- 7
- Category
- Article
- ISSN
- 1660-5446
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It is well-known that functions uEWmlp(R) can be extended by a bounded linear operator E to functions EuC Wm7p(R"), if R is C"-regular and m s M . Here we prove a corresponding result for grid-functions with extension operators E, converging to E and mention some applications.