Catalogue Search | MBRL
Are you sure you want to remove the book from the shelf?
{{itemTitle}}
238
result(s) for
"Direct sum"
Sort by:
Condition pseudospectrum of direct sum of operators on sequence Banach spaces
In this paper, we investigate the relationship between the condition pseudospectrum of linear direct sum of operators in the direct sum of Banach space and its coordinate operators. Besides, we give some remarkable examples as applications of our results.
Journal Article
A seminorm characterization of infinite Banach direct sums
In this paper, the notion of a
Δ
-direct sum of a family of Banach spaces indexed by a set
I
, where
Δ
is a union-closed subnet of
Fin
(
I
)
(the family of all finite subsets of
I
), is introduced. A seminorm characterization of
Δ
-direct sums and some results are presented. Necessary and sufficient conditions are found that a direct sum of a family of Banach spaces is a
Δ
-direct sum. Elements of a direct sum of Banach spaces that are
Δ
-sectionally convergent are introduced and studied. Examples of
Δ
-direct sums and applications of
Δ
-direct sums to Fourier analysis on compact groups are given.
Journal Article
Various Product on Multi Fuzzy Graphs
In this paper, the definition of complement of multi fuzzy graph, direct sum of two multi fuzzy graphs are given and derived some theorems related to them. Also, we examine the different product on multi fuzzy graphs such as Direct product, Cartesian product, Strong product, Composition, Corona product and some properties are analyzed
Journal Article
Operator system structures on the unital direct sum of$C^$ -algebras
This work is motivated by R\\u{a}dulescu's result~\\cite{R˘ad04} on the comparison of C^*-tensor norms on C^*(\\F_n)\\otimes C^*(\\F_n).
¶ For unital C^*-algebras A and B, there are natural inclusions of A and B into the unital free product A\\ast_1 B, the maximal tensor product A\\otimes_{\\max} B and the minimal tensor product A\\otimes_{\\min} B. These inclusions define three operator system structures on the internal sum A+B. Partly using ideas from quantum entanglement theory, we prove various interrelations between these three operator systems. As an application, the present results yield a significant improvement over R\\u{a}dulescu's bound. At the same time, this tight comparison is so general that it cannot be regarded as evidence for the QWEP conjecture.
Journal Article
Triangulated Categories. (AM-148)
The first two chapters of this book offer a modern, self-contained exposition of the elementary theory of triangulated categories and their quotients. The simple, elegant presentation of these known results makes these chapters eminently suitable as a text for graduate students. The remainder of the book is devoted to new research, providing, among other material, some remarkable improvements on Brown's classical representability theorem. In addition, the author introduces a class of triangulated categories\"--the \"well generated triangulated categories\"--and studies their properties. This exercise is particularly worthwhile in that many examples of triangulated categories are well generated, and the book proves several powerful theorems for this broad class. These chapters will interest researchers in the fields of algebra, algebraic geometry, homotopy theory, and mathematical physics.
eBook
Characterizations and properties of the matrices A such that A A ( L ) ( − 1 ) − A ( L ) ( − 1 ) A are nonsingular
In this paper, we consider the co-BD matrices, a class of matrices characterized by the invertibility of
A
A
(
L
)
(
−
1
)
−
A
(
L
)
(
−
1
)
A
, where
A
(
L
)
(
−
1
)
is the Bott-Duffin inverse of A with respect to a subspace L. Different characterizations and properties of this class of matrices are given. Also, we consider some characterizations of the nonsingularity of
A
A
(
L
)
(
−
1
)
−
A
(
L
)
(
−
1
)
A
and
I
n
−
(
A
(
L
)
(
−
1
)
)
2
A
.
Journal Article
Torsion-free modules over commutative domains of Krull dimension one
Let R be a domain of Krull dimension one. We study when the class F of modules over R that are arbitrary direct sums of finitely generated torsion-free modules is closed under direct summands. If R is local, we show that F is closed under direct summands if and only if any indecomposable, finitely generated, torsion-free module has local endomorphism ring. If, in addition, R is noetherian, this is equivalent to saying that the normalization of R is a local ring. If R is an h -local domain of Krull dimension 1 and F_R is closed under direct summands, then the property is inherited by the localizations of R at maximal ideals. Moreover, any localization of R at a maximal ideal, except maybe one, satisfies that any finitely generated ideal is 2 -generated. The converse is true when the domain R is, in addition, integrally closed, or noetherian semilocal, or noetherian with module-finite normalization. Finally, over a commutative domain of finite character and with no restriction on the Krull dimension, we show that the isomorphism classes of countably generated modules in F are determined by their genus.
Journal Article
Generalized inverses, ideals, and projectors in rings
The theory of generalized inverses of matrices and operators is closely connected with projections, i.e., idempotent (bounded) linear transformations. We show that a similar situation occurs in any associative ring 𝓡 with a unit 1 ≠ 0. We prove that generalized inverses in 𝓡 are related to idempotent group endomorphisms ρ : 𝓡 → 𝓡, called projectors. We use these relations to give characterizations and existence conditions for {1}, {2}, and {1, 2}-inverses with any given principal/annihilator ideals. As a consequence, we obtain sufficient conditions for any right/left ideal of 𝓡 to be a principal or an annihilator ideal of an idempotent element of 𝓡. We also study some particular generalized inverses: Drazin and (b, c) inverses, and (e, f) Moore-Penrose, e-core, f-dual core, w-core, dual v-core, right w-core, left dual v-core, and (p, q) inverses in rings with involution.
Journal Article
The direct sum of q-matroids
For classical matroids, the direct sum is one of the most straightforward methods to make a new matroid out of existing ones. This paper defines a direct sum for
q
-matroids, the
q
-analogue of matroids. This is a lot less straightforward than in the classical case, as we will try to convince the reader. With the use of submodular functions and the
q
-analogue of matroid union we come to a definition of the direct sum of
q
-matroids. As a motivation for this definition, we show it has some desirable properties.
Journal Article