The Kato decomposition property

2006 ◽  
pp. 1-53
Keyword(s):  
Decomposition Property

ON ∞-COMPLEX SYMMETRIC OPERATORS

2017 ◽  
Vol 60 (1) ◽  
pp. 35-50
Author(s):  
MUNEO CHŌ ◽  
EUNGIL KO ◽  
JI EUN LEE
Keyword(s):  
Spectral Properties ◽  
Symmetric Operator ◽  
Complex Symmetric Operator ◽  
Decomposition Property ◽  
Complex Symmetric ◽  
Symmetric Operators

AbstractIn this paper, we study spectral properties and local spectral properties of ∞-complex symmetric operators T. In particular, we prove that if T is an ∞-complex symmetric operator, then T has the decomposition property (δ) if and only if T is decomposable. Moreover, we show that if T and S are ∞-complex symmetric operators, then so is T ⊗ S.

scholarly journals Edge ideals of clique clutters of comparability graphs and the normality of monomial ideals

2010 ◽  
Vol 106 (1) ◽  
pp. 88 ◽  
Author(s):  
Luis A. Dupont ◽  
Rafael H. Villarreal
Keyword(s):  
Monomial Ideal ◽  
Lattice Points ◽  
Edge Ideal ◽  
Comparability Graph ◽  
Decomposition Property ◽  
Edge Ideals ◽  
Finite Poset ◽  
Integer Decomposition Property ◽  
Torsion Free ◽  
Min Cut

The normality of a monomial ideal is expressed in terms of lattice points of blocking polyhedra and the integer decomposition property. For edge ideals of clutters this property characterizes normality. Let $G$ be the comparability graph of a finite poset. If $\mathrm{cl}(G)$ is the clutter of maximal cliques of $G$, we prove that $\mathrm{cl}(G)$ satisfies the max-flow min-cut property and that its edge ideal is normally torsion free. Then we prove that edge ideals of complete admissible uniform clutters are normally torsion free.

scholarly journals Characterizing rings by a direct decomposition property of their modules

2006 ◽  
Vol 80 (3) ◽  
pp. 359-366 ◽  
Author(s):  
Dinh Van Huynh ◽  
S. Tariq Rizvi
Keyword(s):  
Projective Module ◽  
Direct Decomposition ◽  
Decomposition Property ◽  
Direct Sum ◽  
Continuous Module

AbstractA module M is said to satisfy the condition (℘*) if M is a direct sum of a projective module and a quasi-continuous module. In an earlier paper, we described the structure of rings over which every (countably generated) right module satisfies (℘*), and it was shown that such a ring is right artinian. In this note some additional properties of these rings are obtained. Among other results, we show that a ring over which all right modules satisfy (℘*) is also left artinian, but the property (℘*) is not left-right symmetric.

C* -Algebras of Real Rank Zero Whose K0's are not Riesz Groups

1996 ◽  
Vol 39 (4) ◽  
pp. 429-437 ◽  
Author(s):  
K. R. Goodearl
Keyword(s):  
Real Rank ◽  
Riesz Decomposition Property ◽  
Real Rank Zero ◽  
Decomposition Property ◽  
Rank Zero ◽  
C Algebras ◽  
Finite Dimensional ◽  
Riesz Decomposition ◽  
Stably Finite ◽  
The Riesz Decomposition Property

AbstractExamples are constructed of stably finite, imitai, separable C* -algebras A of real rank zero such that the partially ordered abelian groups K0(A) do not satisfy the Riesz decomposition property. This contrasts with the result of Zhang that projections in C* -algebras of real rank zero satisfy Riesz decomposition. The construction method also produces a stably finite, unital, separable C* -algebra of real rank zero which has the same K-theory as an approximately finite dimensional C*-algebra, but is not itself approximately finite dimensional.

scholarly journals Decompositions of Weakly Compact Valued Integrable Multifunctions

Mathematics ◽  
2020 ◽  
Vol 8 (6) ◽  
pp. 863 ◽  
Author(s):  
Luisa Di Piazza ◽  
Kazimierz Musiał
Keyword(s):  
Banach Space ◽  
Separable Banach Space ◽  
Compact Convex ◽  
Weakly Compact ◽  
Seminal Paper ◽  
Decomposition Property ◽  
Short Overview ◽  
Decomposition Theorems ◽  
State Of Art

We give a short overview on the decomposition property for integrable multifunctions, i.e., when an “integrable in a certain sense” multifunction can be represented as a sum of one of its integrable selections and a multifunction integrable in a narrower sense. The decomposition theorems are important tools of the theory of multivalued integration since they allow us to see an integrable multifunction as a translation of a multifunction with better properties. Consequently, they provide better characterization of integrable multifunctions under consideration. There is a large literature on it starting from the seminal paper of the authors in 2006, where the property was proved for Henstock integrable multifunctions taking compact convex values in a separable Banach space X. In this paper, we summarize the earlier results, we prove further results and present tables which show the state of art in this topic.

Decomposition property of the Slater determinant

1965 ◽  
Vol 184 (2) ◽  
pp. 175-180
Author(s):  
Edward B. Jay
Keyword(s):  
Slater Determinant ◽  
Decomposition Property
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