共查询到20条相似文献,搜索用时 15 毫秒
1.
Let $
\mathfrak{S}
$
\mathfrak{S}
be a locally compact semigroup, ω be a weight function on $
\mathfrak{S}
$
\mathfrak{S}
, and M
a
($
\mathfrak{S}
$
\mathfrak{S}
, ω) be the weighted semigroup algebra of $
\mathfrak{S}
$
\mathfrak{S}
. Let L
0∞ ($
\mathfrak{S}
$
\mathfrak{S}
; M
a
($
\mathfrak{S}
$
\mathfrak{S}
, ω)) be the C*-algebra of all M
a
($
\mathfrak{S}
$
\mathfrak{S}
, ω)-measurable functions g on $
\mathfrak{S}
$
\mathfrak{S}
such that g/ω vanishes at infinity. We introduce and study a strict topology β
1($
\mathfrak{S}
$
\mathfrak{S}
, ω) on M
a
($
\mathfrak{S}
$
\mathfrak{S}
, ω) and show that the Banach space L
0∞ ($
\mathfrak{S}
$
\mathfrak{S}
; M
a
($
\mathfrak{S}
$
\mathfrak{S}
, ω)) can be identified with the dual of M
a
($
\mathfrak{S}
$
\mathfrak{S}
, ω) endowed with β
1($
\mathfrak{S}
$
\mathfrak{S}
, ω). We finally investigate some properties of the locally convex topology β
1($
\mathfrak{S}
$
\mathfrak{S}
, ω) on M
a
($
\mathfrak{S}
$
\mathfrak{S}
, ω). 相似文献
2.
Spiros A. Argyros Irene Deliyanni Andreas G. Tolias 《Israel Journal of Mathematics》2011,181(1):65-110
We provide a characterization of the Banach spaces X with a Schauder basis (e
n
)
n∈ℕ which have the property that the dual space X* is naturally isomorphic to the space L
diag(X) of diagonal operators with respect to (e
n
)
n∈ℕ. We also construct a Hereditarily Indecomposable Banach space $
\mathfrak{X}
$
\mathfrak{X}
D with a Schauder basis (e
n
)
n∈ℕ such that $
\mathfrak{X}
$
\mathfrak{X}
*D is isometric to L
diag($
\mathfrak{X}
$
\mathfrak{X}
D) with these Banach algebras being Hereditarily Indecomposable. Finally, we show that every T ∈ L
diag($
\mathfrak{X}
$
\mathfrak{X}
D) is of the form T = λI + K, where K is a compact operator. 相似文献
3.
K. Zh. Kudaibergenov 《Siberian Advances in Mathematics》2010,20(1):58-67
We introduce the notion of a superstructure over a model. This is a generalization of the notion of the hereditarily finite
superstructure ℍ$
\mathbb{F}\mathfrak{M}
$
\mathbb{F}\mathfrak{M}
over a model $
\mathfrak{M}
$
\mathfrak{M}
. We consider the question on cardinalities of definable (interpretable) sets in superstructures over λ-homogeneous and λ-saturated models. 相似文献
4.
Let G be a finite group, and let $
\mathfrak{F}
$
\mathfrak{F}
be a formation of finite groups. We say that a subgroup H of G is $
\mathfrak{F}_h
$
\mathfrak{F}_h
-normal in G if there exists a normal subgroup T of G such that HT is a normal Hall subgroup of G and (H ∩ T)H
G
/H
G
is contained in the $
\mathfrak{F}
$
\mathfrak{F}
-hypercenter $
Z_\infty ^\mathfrak{F}
$
Z_\infty ^\mathfrak{F}
(G/H
G
) of G/H
G
. In this paper, we obtain some results about the $
\mathfrak{F}_h
$
\mathfrak{F}_h
-normal subgroups and then use them to study the structure of finite groups. 相似文献
5.
V. G. Puzarenko 《Siberian Advances in Mathematics》2010,20(2):128-154
We study some properties of a $
\mathfrak{c}
$
\mathfrak{c}
-universal semilattice $
\mathfrak{A}
$
\mathfrak{A}
with the cardinality of the continuum, i.e., of an upper semilattice of m-degrees. In particular, it is shown that the quotient semilattice of such a semilattice modulo any countable ideal will be
also $
\mathfrak{c}
$
\mathfrak{c}
-universal. In addition, there exists an isomorphism
$
\mathfrak{A}
$
\mathfrak{A}
such that $
{\mathfrak{A} \mathord{\left/
{\vphantom {\mathfrak{A} {\iota \left( \mathfrak{A} \right)}}} \right.
\kern-\nulldelimiterspace} {\iota \left( \mathfrak{A} \right)}}
$
{\mathfrak{A} \mathord{\left/
{\vphantom {\mathfrak{A} {\iota \left( \mathfrak{A} \right)}}} \right.
\kern-\nulldelimiterspace} {\iota \left( \mathfrak{A} \right)}}
will be also $
\mathfrak{c}
$
\mathfrak{c}
-universal. Furthermore, a property of the group of its automorphisms is obtained. To study properties of this semilattice,
the technique and methods of admissible sets are used. More exactly, it is shown that the semilattice of mΣ-degrees $
L_{m\Sigma }^{\mathbb{H}\mathbb{F}\left( S \right)}
$
L_{m\Sigma }^{\mathbb{H}\mathbb{F}\left( S \right)}
on the hereditarily finite superstructure $
\mathbb{H}\mathbb{F}
$
\mathbb{H}\mathbb{F}
(S) over a countable set S will be a $
\mathfrak{c}
$
\mathfrak{c}
-universal semilattice with the cardinality of the continuum. 相似文献
6.
RenCai Lü 《中国科学A辑(英文版)》2009,52(3):517-525
In this paper, the Harish-Chandra modules and Verma modules over Block algebra $
\mathfrak{L}
$
\mathfrak{L}
[G] are investigated. More precisely, the irreducibility of the Verma modules over $
\mathfrak{L}
$
\mathfrak{L}
[G] is completely determined, and the Harish-Chandra modules over $
\mathfrak{L}
$
\mathfrak{L}
[ℤ] are classified. 相似文献
7.
V. I. Gorbachuk V. M. Gorbachuk 《P-Adic Numbers, Ultrametric Analysis, and Applications》2010,2(2):114-121
Let A be a closed linear operator on a Banach space $
\mathfrak{B}
$
\mathfrak{B}
over the field Ω of complex p-adic numbers having an inverse operator defined on the whole $
\mathfrak{B}
$
\mathfrak{B}
, and f be a locally holomorphic at 0 $
\mathfrak{B}
$
\mathfrak{B}
-valued vector function. The problem of existence and uniqueness of a locally holomorphic at 0 solution of the differential
equation y
(m) − Ay = f is considered in this paper. In particular, it is shown that this problem is solvable under the condition $
\mathop {\lim }\limits_{n \to \infty } \sqrt[n]{{\left\| {A^{ - n} } \right\|}}
$
\mathop {\lim }\limits_{n \to \infty } \sqrt[n]{{\left\| {A^{ - n} } \right\|}}
= 0. It is proved also that if the vector-function f is entire, then there exists a unique entire solution of this equation. Moreover, the necessary and sufficient conditions
for the Cauchy problem for such an equation to be correctly posed in the class of locally holomorphic functions are presented. 相似文献
8.
A. V. Parfenenkov 《Proceedings of the Steklov Institute of Mathematics》2009,266(Z1):194-204
We study the class $
\mathfrak{P}_n
$
\mathfrak{P}_n
of algebraic polynomials P
n
(x, y) in two variables of total degree n whose uniform norm on the unit circle Γ1 centered at the origin is at most 1: $
\left\| {P_n } \right\|_{C(\Gamma _1 )}
$
\left\| {P_n } \right\|_{C(\Gamma _1 )}
≤ 1. The extension of polynomials from the class $
\mathfrak{P}_n
$
\mathfrak{P}_n
to the plane with the least uniform norm on the concentric circle Γ
r
of radius r is investigated. It is proved that the values θ
n
(r) of the best extension of the class $
\mathfrak{P}_n
$
\mathfrak{P}_n
satisfy the equalities θ
n
(r) = r
n
for r > 1 and θ
n
(r) = r
n−1 for 0 < r < 1. 相似文献
9.
The set of all m × n Boolean matrices is denoted by $
\mathbb{M}
$
\mathbb{M}
m,n
. We call a matrix A ∈ $
\mathbb{M}
$
\mathbb{M}
m,n
regular if there is a matrix G ∈ $
\mathbb{M}
$
\mathbb{M}
n,m
such that AGA = A. In this paper, we study the problem of characterizing linear operators on $
\mathbb{M}
$
\mathbb{M}
m,n
that strongly preserve regular matrices. Consequently, we obtain that if min{m, n} ⩽ 2, then all operators on $
\mathbb{M}
$
\mathbb{M}
m,n
strongly preserve regular matrices, and if min{m, n} ⩾ 3, then an operator T on $
\mathbb{M}
$
\mathbb{M}
m,n
strongly preserves regular matrices if and only if there are invertible matrices U and V such that T(X) = UXV for all X ε $
\mathbb{M}
$
\mathbb{M}
m,n
, or m = n and T(X) = UX
T
V for all X ∈ $
\mathbb{M}
$
\mathbb{M}
n
. 相似文献
10.
S. S. Kutateladze 《Siberian Mathematical Journal》2009,50(5):887-897
Under study is the new class of geometrical extremal problems in which it is required to achieve the best result in the presence
of conflicting goals; e.g., given the surface area of a convex body $
\mathfrak{x}
$
\mathfrak{x}
, we try to maximize the volume of $
\mathfrak{x}
$
\mathfrak{x}
and minimize the width of $
\mathfrak{x}
$
\mathfrak{x}
simultaneously. These problems are addressed along the lines of multiple criteria decision making. We describe the Pareto-optimal
solutions of isoperimetric-type vector optimization problems on using the techniques of the space of convex sets, linear majorization,
and mixed volumes. 相似文献
11.
We develop a general technique to study completeness in a metrically generated construct X, the objects of which can be isomorphically
described as sets endowed with a gauge of quasi metrics, saturated in a certain way. Our approach depends on a given functor
F on X, describing the transition to some known topological construct A in which there already exists a completion theory
described by some reflector R and for which also the associated firm class of morphisms $
\mathfrak{L}
$
\mathfrak{L}
(R) is known. This functor will permit to “lift” the notion of completeness from A to X. We describe sufficient conditions
on R and F, ensuring that the lifting produces a completion theory RF for the construct X0 of T
0 objects and that the associated firm class of morphisms can be derived from $
\mathfrak{L}
$
\mathfrak{L}
(R). Application of this technique to concrete examples results in many interesting completion theories and provides us with
a far better understanding of several existing ones. 相似文献
12.
The existence of a faithful modular representation of a left module $
\mathfrak{X}
$
\mathfrak{X}
over a C*-algebra $
\mathfrak{A}_\#
$
\mathfrak{A}_\#
possessing sufficiently many traces is proved. 相似文献
13.
Let M be a subset of r-dimensional vector space Vτ (F2) over a finite field F2, consisting of n nonzero vectors, such that every t vectors of M are linearly independent over F2. Then M is called (n, t)-linearly independent array of length n over Vτ(F2). The (n, t)-linearly independent array M that has the maximal number of elements is called the maximal (r, t)-linearly independent array, and the maximal number is denoted by M(r, t). It is an interesting combinatorial structure, which has many applications in cryptography and coding theory. It can be used to construct orthogonal arrays, strong partial balanced designs. It can also be used to design good linear codes, In this paper, we construct a class of maximal (r, t)-linearly independent arrays of length r + 2, and provide some enumerator theorems. 相似文献
14.
A. V. Stolyarov 《Russian Mathematics (Iz VUZ)》2010,54(11):56-65
In this paper, the following results are obtained: 1) It is proved that, in the fourth order differential neighborhood, a
regular hypersurface V
n−1 embedded into a projective-metric space K
n
, n ≥ 3, intrinsically induces a dual projective-metric space $
\bar K_n
$
\bar K_n
. 2) An invariant analytical condition is established under which a normalization of a hypersurface V
n−1 ⊂ K
n
(a tangential hypersurface $
\bar V_{n - 1}
$
\bar V_{n - 1}
⊂ $
\bar K_n
$
\bar K_n
) by quasitensor fields H
n
i
, H
i
($
\bar H_n^i
$
\bar H_n^i
, $
\bar H_i
$
\bar H_i
) induces a Riemannian space of constant curvature. If the two conditions are fulfilled simultaneously, the spaces R
n−1 and $
\bar R_{n - 1}
$
\bar R_{n - 1}
are spaces of the same constant curvature $
K = - \tfrac{1}
{c}
$
K = - \tfrac{1}
{c}
. 3) Geometric interpretations of the obtained analytical conditions are given. 相似文献
15.
16.
We present a few results and problems related to spaces of continuous functions with the topology of pointwise convergence
and the classes of LΣ(≤ ω)-spaces; in particular, we prove that every Gul’ko compact space of cardinality less or equal to $
\mathfrak{c}
$
\mathfrak{c}
is an LΣ(≤ ω)-space. 相似文献
17.
In this note we construct a function φ in L2(Bn,dμ) which is unbounded on any neighborhood of each boundary point of Bn such that Tφ is a trace class operator on weighted Bergman space Lα2(Bn,dμ) for several complex variables. 相似文献
18.
A metric space M is said to have the fibered approximation property in dimension n (briefly, M ∈ FAP(n)) if for any ɛ > 0, m ≥ 0 and any map g: $
\mathbb{I}
$
\mathbb{I}
m
× $
\mathbb{I}
$
\mathbb{I}
n
→ M there exists a map g′: $
\mathbb{I}
$
\mathbb{I}
m
× $
\mathbb{I}
$
\mathbb{I}
n
→ M such that g′ is ɛ-homotopic to g and dim g′ ({z} × $
\mathbb{I}
$
\mathbb{I}
n
) ≤ n for all z ∈ $
\mathbb{I}
$
\mathbb{I}
m
. The class of spaces having the FAP(n)-property is investigated in this paper. The main theorems are applied to obtain generalizations of some results due to Uspenskij
[11] and Tuncali-Valov [10]. 相似文献
19.
Wenhua Zhao 《Central European Journal of Mathematics》2010,8(6):1132-1155
We first propose a generalization of the notion of Mathieu subspaces of associative algebras $
\mathcal{A}
$
\mathcal{A}
, which was introduced recently in [Zhao W., Generalizations of the image conjecture and the Mathieu conjecture, J. Pure Appl.
Algebra, 2010, 214(7), 1200–1216] and [Zhao W., Mathieu subspaces of associative algebras], to $
\mathcal{A}
$
\mathcal{A}
-modules $
\mathcal{M}
$
\mathcal{M}
. The newly introduced notion in a certain sense also generalizes the notion of submodules. Related with this new notion,
we also introduce the sets σ(N) and τ(N) of stable elements and quasi-stable elements, respectively, for all R-subspaces N of $
\mathcal{A}
$
\mathcal{A}
-modules $
\mathcal{M}
$
\mathcal{M}
, where R is the base ring of $
\mathcal{A}
$
\mathcal{A}
. We then prove some general properties of the sets σ(N) and τ(N). Furthermore, examples from certain modules of the quasi-stable algebras [Zhao W., Mathieu subspaces of associative algebras], matrix algebras over fields and polynomial algebras are also studied. 相似文献
20.
We classify deformations of the standard embedding of the Lie superalgebra $
\mathcal{K}
$
\mathcal{K}
(2) of contact vector fields on the (1, 2)-dimensional supercircle into the Lie superalgebra SΨD(S
1|2
) of pseudodifferential operators on the supercircle S
1|2
. The proposed approach leads to the deformations of the central charge induced on $
\mathcal{K}
$
\mathcal{K}
(2) by the canonical central extension of SΨD(S
1|2
). 相似文献