Reflexivity and approximate reflexivity for bounded Boolean algebras of projections

Hadwin, Don
Orhon, Mehmet
Let K be a compact Hausdorff space. It is proven that any bounded unital representation m of C(K) on a Banach space X has the property that the closure of m(C(K)) in the weak operator topology is a reflexive operator algebra. As a consequence, it is shown that if is an arbitrary bounded Boolean algebra of bounded projections on a Banach space X, then AlgLat() is the weak operator topology closure of the linear span of . These generalize the work of several authors. As a corollary, an alternate proof of a theorem of Bade is obtained. In addition, approximate reflexivity results are obtained for the norm closures of m(C(K)) and span().
Journal of Functional Analysis


ERKIP, AK; SCHROHE, E (Elsevier BV, 1992-10-01)
Normal solvability is shown for a class of boundary value problems on Riemannian manifolds with noncompact boundary using a concept of weighted pseudodifferential operators and weighted Sobolev spaces together with Lopatinski-Shapiro type boundary conditions. An essential step is to show that the standard normal derivative defined in terms of the Riemannian metric is in fact a weighted pseudodifferential operator of the considered class provided the metric is compatible with the symbols.
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Dosiev, Anar (Elsevier BV, 2008-10-01)
In this paper we propose a representation theorem for local operator spaces which extends Ruan's representation theorem for operator spaces. Based upon this result, we introduce local operator systems which are locally convex versions of the operator systems and prove Stinespring theorem for local operator systems. A local operator C*-algebra is an example of a local operator system. Finally, we investigate the injectivity in both local operator space and local operator system senses, and prove locally conv...
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Celebi, AO; Kalantarov, VK; Polat, Mustafa Uğur (Elsevier BV, 1999-09-20)
We consider the periodic initial-boundary value problem for a multidimensional generalized Benjamin-Bona-Mahony equation. We show the existence of the global attractor with a finite Fractal dimension and the existence of the exponential attractor for the corresponding semigroup. (C) 1999 Academic Press.
Basis in nuclear Frechet spaces
Erkurşun, Nazife; Nurlu, Mehmet Zafer; Department of Mathematics (2006)
Existence of basis in locally convex space has been an important problem in functional analysis for more than 40 years. In this thesis the conditions for the existence of basis are examined. These thesis consist of three parts. The first part is about the exterior interpolative conditions. The second part deals with the inner interpolative conditions on nuclear frechet space. These are sufficient conditions on existence of basis. In the last part, it is shown that for a regular nuclear Köthe space the inner...
MİKKELSEN, CCK; Manguoğlu, Murat (Society for Industrial & Applied Mathematics (SIAM), 2008-01-01)
The truncated SPIKE algorithm is a parallel solver for linear systems which are banded and strictly diagonally dominant by rows. There are machines for which the current implementation of the algorithm is faster and scales better than the corresponding solver in ScaLAPACK (PDDBTRF/PDDBTRS). In this paper we prove that the SPIKE matrix is strictly diagonally dominant by rows with a degree no less than the original matrix. We establish tight upper bounds on the decay rate of the spikes as well as the truncati...
Citation Formats
D. Hadwin and M. Orhon, “Reflexivity and approximate reflexivity for bounded Boolean algebras of projections,” Journal of Functional Analysis, pp. 348–358, 1989, Accessed: 00, 2020. [Online]. Available: