Weak Operator Topology
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High Quality Content by WIKIPEDIA articles! In functional analysis, the weak operator topology, often abbreviated WOT, is the weakest topology on the set of bounded operators on a Hilbert space H such that the functional sending an operator T to the complex number is continuous for any vectors x and y in the Hilbert space. The strong operator topology, or SOT, on B(H) is the topology of pointwise convergence. Because the inner product is a continuous function, the SOT is stronger than WOT. The following example shows that this inclusion is strict. Let H = 2(N) and consider the sequence {Tn} where T is the unilateral shift. An application of Cauchy-Schwarz shows that Tn 0 in WOT. But clearly Tn does not converge to 0 in SOT.
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GarantieWeitere Informationen
- Allgemeine Informationen
- GTIN 09786130363437
- Editor Lambert M. Surhone, Miriam T. Timpledon, Susan F. Marseken
- Sprache Englisch
- Größe H220mm x B150mm x T5mm
- Jahr 2010
- EAN 9786130363437
- Format Fachbuch
- ISBN 978-613-0-36343-7
- Titel Weak Operator Topology
- Untertitel Functional Analysis, Topology, Bounded Operator, Functional (mathematics), Continuous Function (topology), Operator Topology, Strong Operator Topology, Polarization Identity
- Gewicht 137g
- Herausgeber VDM Verlag Dr. Müller e.K.
- Anzahl Seiten 80
- Genre Mathematik
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