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Unusual Traces on Operator Ideals
Mathematische Nachrichten, 1987Let H be a separable Hilbert space and B(H) (resp. \(B_ 0(H))\) the space of all bounded linear operators (resp. compact operators) defined on H. Given an ideal J in \(B_ 0(H)\) a trace on J is a linear functional \(\tau\) on J so that (1) \(\tau (P)=1\) if P is a rank one projection, (2) \(\tau (XY)=\tau (YX)\) if \(X\in J\) and \(Y\in B(H).\) We say ...
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Invariant Ideals of Positive Operators
SIAM Review, 1974This paper gives a systematic treatment of generalizations of the Perron–Frobenius theorems for nonnegative matrices to semigroups of positive operators acting on ordered Banach spaces with order units.
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Ideals in algebras of unbounded operators. II
Mathematische Nachrichten, 1979AbstractA general procedure is given to get ideals in algebras of unbounded operators starting with ideals in ℬ︁(ℋ︁). Algebraical and topological properties of ideals obtained in this manner from the well‐known symmetrically‐normed ideals Sϕ(ℋ︁) are described.
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2018
In this chapter, we apply some of the operations of Appendix A to monomial ideals. We have already seen this theme for sums and products in Exercises 1.3.12 and 1.3.13. In Section 2.1 we show, for instance, that intersections of monomial ideals are monomial ideals.
W. Frank Moore +2 more
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In this chapter, we apply some of the operations of Appendix A to monomial ideals. We have already seen this theme for sums and products in Exercises 1.3.12 and 1.3.13. In Section 2.1 we show, for instance, that intersections of monomial ideals are monomial ideals.
W. Frank Moore +2 more
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Circuits, Systems, and Signal Processing, 1984
The definitions and properties of various ideals of a nest algebra are reviewed. These correspond to strengthenings of the concept of causality. The interrelationships between these concepts are examined. An open question concerning these ideals is settled, namely that the strongly strictly causal operators form the largest of the classes commonly ...
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The definitions and properties of various ideals of a nest algebra are reviewed. These correspond to strengthenings of the concept of causality. The interrelationships between these concepts are examined. An open question concerning these ideals is settled, namely that the strongly strictly causal operators form the largest of the classes commonly ...
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2020
Ideale in der Algebra aller beschränkten linearen Operatoren eines Hilbertraumes H in sich sind ein viel studiertes Objekt. Ist H separabel, so sind alle echten Ideale in dem Ideal K(H) der kompakten Operatoren enthalten. Seit einer grundlegenden Arbeit von J.W.Calkin aus 1941 weiß man, dass Ideale in K(H) bijektiv gewissen Räumen monotoner Nullfolgen ...
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Ideale in der Algebra aller beschränkten linearen Operatoren eines Hilbertraumes H in sich sind ein viel studiertes Objekt. Ist H separabel, so sind alle echten Ideale in dem Ideal K(H) der kompakten Operatoren enthalten. Seit einer grundlegenden Arbeit von J.W.Calkin aus 1941 weiß man, dass Ideale in K(H) bijektiv gewissen Räumen monotoner Nullfolgen ...
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