共查询到20条相似文献,搜索用时 46 毫秒
1.
Recently, Blecher and Kashyap have generalized the notion of W
*-modules over von Neumann algebras to the setting where the operator algebras are σ closed algebras of operators on a Hilbert space. They call these modules weak* rigged modules. We characterize the weak* rigged modules over nest algebras. We prove that Y is a right weak* rigged module over a nest algebra Alg(M){\rm{Alg}(\mathcal M)} if and only if there exists a completely isometric normal representation F{\Phi } of Y and a nest algebra Alg(N){\rm{Alg}(\mathcal N)} such that Alg(N) F(Y)Alg(M) ì F(Y){\rm{Alg}(\mathcal N) \Phi (Y)\rm{Alg}(\mathcal M)\subset \Phi (Y)} while F(Y){\Phi (Y)} is implemented by a continuous nest homomorphism from M{\mathcal M} onto N{\mathcal N} . We describe some properties which are preserved by continuous CSL homomorphisms. 相似文献
2.
For a simple connected undirected graph G, c(G), cf(G), Yf(G), f(G), ?G(G){\chi(G), \chi_f(G), \Psi_f(G), \phi(G), \partial \Gamma (G)} and Ψ(G) denote respectively the chromatic number, fall chromatic number (assuming that it exists for G), fall achromatic number, b-chromatic number, partial Grundy number and achromatic number of G. It is shown in Dunbar et al. (J Combin Math & Combin Comput 33:257–273, 2000) that for any graph G for which fall coloring exists, c(G) £ cf(G) £ Yf (G) £ f(G) £ ?G(G) £ Y(G){\chi (G)\leq \chi_f(G) \leq \Psi_f (G) \leq \phi(G) \leq \partial \Gamma (G)\leq \Psi (G)} . In this paper, we exhibit an infinite family of graphs G with a strictly increasing color chain: c(G) < cf(G) < Yf (G) < f(G) < ?G(G) < Y(G){\chi (G) < \chi_f(G) < \Psi_f (G) < \phi(G) < \partial \Gamma (G) < \Psi (G)} . The existence of such a chain was raised by Dunbar et al. 相似文献
3.
Wojciech Jaworski 《Monatshefte für Mathematik》2008,336(4):135-144
Given a locally compact group G, let
J(G){\cal J}(G)
denote the set of closed left ideals in L
1(G), of the form J
μ = [L1(G) * (δ
e
− μ)]−, where μ is a probability measure on G. Let
Jd(G)={\cal J}_d(G)=
{Jm;m is discrete}\{J_{\mu};\mu\ {\rm is discrete}\}
,
Ja(G)={Jm;m is absolutely continuous}{\cal J}_a(G)=\{J_{\mu};\mu\ {\rm is absolutely continuous}\}
. When G is a second countable [SIN] group, we prove that
J(G)=Jd(G){\cal J}(G)={\cal J}_d(G)
and that
Ja(G){\cal J}_a(G)
, being a proper subset of
J(G){\cal J}(G)
when G is nondiscrete, contains every maximal element of
J(G){\cal J}(G)
. Some results concerning the ideals J
μ in general locally compact second countable groups are also obtained. 相似文献
4.
Let
G ì \mathbb C G \subset {\mathbb C} be a finite region bounded by a Jordan curve L: = ?G L: = \partial G , let
W: = \textext[`(G)] \Omega : = {\text{ext}}\bar{G} (with respect to
[`(\mathbb C)] {\overline {\mathbb C}} ), $ \Delta : = \left\{ {z:\left| z \right| > 1} \right\} $ \Delta : = \left\{ {z:\left| z \right| > 1} \right\} , and let w = F(z) w = \Phi (z) be a univalent conformal mapping of Ω onto Δ normalized by $ \Phi \left( \infty \right) = \infty, \;\Phi '\left( \infty \right) > 0 $ \Phi \left( \infty \right) = \infty, \;\Phi '\left( \infty \right) > 0 . By A
p
(G); p > 0; we denote a class of functions f analytic in G and satisfying the condition
|| f ||App(G): = òG | f(z) |pdsz < ¥, \left\| f \right\|_{Ap}^p(G): = \int\limits_G {{{\left| {f(z)} \right|}^p}d{\sigma_z} < \infty, } 相似文献
5.
Given 1 ≤ p < ∞, a compact abelian group G and a p-multiplier ${\psi : \Gamma \to {\mathbb C}}
6.
Giorgio Gnecco 《4OR: A Quarterly Journal of Operations Research》2011,9(1):103-106
This is a summary of the author’s PhD thesis, supervised by Marcello Sanguineti and defended on April 2, 2009 at Università
degli Studi di Genova. The thesis is written in English and a copy is available from the author upon request. Functional optimization
problems arising in Operations Research are investigated. In such problems, a cost functional Φ has to be minimized over an admissible set S of d-variable functions. As, in general, closed-form solutions cannot be derived, suboptimal solutions are searched for, having
the form of variable-basis functions, i.e., elements of the set span
n
G of linear combinations of at most n elements from a set G of computational units. Upper bounds on inff ? S ?spann GF(f)-inff ? SF(f){\inf_{f \in S \cap {\rm span}_n\, G}\Phi(f)-\inf_{f \in S}\Phi(f)} are obtained. Conditions are derived, under which the estimates do not exhibit the so-called “curse of dimensionality” in
the number n of computational units, when the number d of variables grows. The problems considered include dynamic optimization, team optimization, and supervised learning from
data. 相似文献
7.
E. L. Bashkirov 《Archiv der Mathematik》2002,79(5):321-327
We study the subgroups of
GLn(D) (n \geqq 3) GL_{n}(D) (n \geqq 3) over a skew field of quaternions D that comprise the subgroup of the unitary group Un(A, F) U_{n}(A, \Phi) over a subsfield
A \subseteqq D A \subseteqq D generated by all transvections in Un(A, F) U_{n}(A, \Phi) . 相似文献
8.
Masato Kikuchi 《Mathematische Zeitschrift》2010,265(4):865-887
Let ${\Phi : \mathbb{R} \to [0, \infty)}
9.
We show that the result on multipliers of Orlicz spaces holds in general. Namely, under the assumption that three Young functions Φ1, Φ2 and Φ, generating corresponding Orlicz spaces, satisfy the estimate ${\Phi^{-1}(u) \leq C \Phi_1^{-1}(u)\, \Phi_2^{-1}(u)}
10.
Let M{\mathcal M} be a σ-finite von Neumann algebra and
\mathfrak A{\mathfrak A} a maximal subdiagonal algebra of M{\mathcal M} with respect to a faithful normal conditional expectation F{\Phi} . Based on Haagerup’s noncommutative L
p
space Lp(M){L^p(\mathcal M)} associated with M{\mathcal M} , we give a noncommutative version of H
p
space relative to
\mathfrak A{\mathfrak A} . If h
0 is the image of a faithful normal state j{\varphi} in L1(M){L^1(\mathcal M)} such that j°F = j{\varphi\circ \Phi=\varphi} , then it is shown that the closure of
{\mathfrak Ah0\frac1p}{\{\mathfrak Ah_0^{\frac1p}\}} in Lp(M){L^p(\mathcal M)} for 1 ≤ p < ∞ is independent of the choice of the state preserving F{\Phi} . Moreover, several characterizations for a subalgebra of the von Neumann algebra M{\mathcal M} to be a maximal subdiagonal algebra are given. 相似文献
11.
Christoph Lienau 《Mathematische Annalen》2011,351(2):403-410
For a real linear algebraic group G let A(G){\mathcal{A}(G)} be the algebra of analytic vectors for the left regular representation of G on the space of superexponentially decreasing functions. We present an explicit Dirac sequence in A(G){\mathcal{A}(G)}. Since A(G){\mathcal{A}(G)} acts on E for every Fréchet-representation (π, E) of moderate growth, this yields an elementary proof of a result of Nelson that the space of analytic vectors is dense in
E. 相似文献
12.
A proper vertex colouring of a graph G is 2-frugal (resp. linear) if the graph induced by the vertices of any two colour classes is of maximum degree 2 (resp. is a forest of paths). A graph
G is 2-frugally (resp. linearly) L-colourable if for a given list assignment
L:V(G)? 2\mathbb N{L:V(G)\mapsto 2^{\mathbb N}} , there exists a 2-frugal (resp. linear) colouring c of G such that c(v) ? L(v){c(v) \in L(v)} for all v ? V(G){v\in V(G)} . If G is 2-frugally (resp. linearly) L-list colourable for any list assignment such that |L(v)| ≥ k for all v ? V(G){v\in V(G)}, then G is 2-frugally (resp. linearly) k-choosable. In this paper, we improve some bounds on the 2-frugal choosability and linear choosability of graphs with small maximum
average degree. 相似文献
13.
An edge coloring is called vertex-distinguishing if every two distinct vertices are incident to different sets of colored edges. The minimum number of colors required for
a vertex-distinguishing proper edge coloring of a simple graph G is denoted by c¢vd(G){\chi'_{vd}(G)}. It is proved that c¢vd(G) £ D(G)+5{\chi'_{vd}(G)\leq\Delta(G)+5} if G is a connected graph of order n ≥ 3 and
s2(G) 3 \frac2n3{\sigma_{2}(G)\geq\frac{2n}{3}}, where σ
2(G) denotes the minimum degree sum of two nonadjacent vertices in G. 相似文献
14.
Kewen Zhao 《Monatshefte für Mathematik》2009,20(1):279-293
Let G be a simple graph with n vertices. For any v ? V(G){v \in V(G)} , let N(v)={u ? V(G): uv ? E(G)}{N(v)=\{u \in V(G): uv \in E(G)\}} , NC(G) = min{|N(u) èN(v)|: u, v ? V(G){NC(G)= \min \{|N(u) \cup N(v)|: u, v \in V(G)} and
uv \not ? E(G)}{uv \not \in E(G)\}} , and NC2(G) = min{|N(u) èN(v)|: u, v ? V(G){NC_2(G)= \min\{|N(u) \cup N(v)|: u, v \in V(G)} and u and v has distance 2 in E(G)}. Let l ≥ 1 be an integer. A graph G on n ≥ l vertices is [l, n]-pan-connected if for any u, v ? V(G){u, v \in V(G)} , and any integer m with l ≤ m ≤ n, G has a (u, v)-path of length m. In 1998, Wei and Zhu (Graphs Combinatorics 14:263–274, 1998) proved that for a three-connected graph on n ≥ 7 vertices, if NC(G) ≥ n − δ(G) + 1, then G is [6, n]-pan-connected. They conjectured that such graphs should be [5, n]-pan-connected. In this paper, we prove that for a three-connected graph on n ≥ 7 vertices, if NC
2(G) ≥ n − δ(G) + 1, then G is [5, n]-pan-connected. Consequently, the conjecture of Wei and Zhu is proved as NC
2(G) ≥ NC(G). Furthermore, we show that the lower bound is best possible and characterize all 2-connected graphs with NC
2(G) ≥ n − δ(G) + 1 which are not [4, n]-pan-connected. 相似文献
15.
Cyril Houdayer 《Mathematische Annalen》2010,346(4):969-989
We give examples of non-amenable infinite conjugacy classes groups Γ with the Haagerup property, weakly amenable with constant
Λcb(Γ) = 1, for which we show that the associated II1 factors L(Γ) are strongly solid, i.e. the normalizer of any diffuse amenable subalgebra P ì L(G){P \subset L(\Gamma)} generates an amenable von Neumann algebra. Nevertheless, for these examples of groups Γ, L(Γ) is not isomorphic to any interpolated free group factor L(F
t
), for 1 < t ≤ ∞. 相似文献
16.
Let G be a finite group. We say that G is a T0-group, if its Frattini quotient group G/F(G)G/\Phi (G) is a T-group, where by a T-group we mean a group in which every subnormal subgroup is normal. We determine the structure of a non T0-group G all of whose proper subgroups are T0-groups. 相似文献
17.
Harald Grobner 《Monatshefte für Mathematik》2010,139(1):335-340
Let
G/\mathbb Q{G/\mathbb Q} be the simple algebraic group Sp(n, 1) and G = G(N){\Gamma=\Gamma(N)} a principal congruence subgroup of level N ≥ 3. Denote by K a maximal compact subgroup of the real Lie group
G(\mathbb R){G(\mathbb R)} . Then a double quotient
G\G(\mathbb R)/K{\Gamma\backslash G(\mathbb R)/K} is called an arithmetically defined, quaternionic hyperbolic n-manifold. In this paper we give an explicit growth condition for the dimension of cuspidal cohomology
H2ncusp(G\G(\mathbb R)/K,E){H^{2n}_{cusp}(\Gamma\backslash G(\mathbb R)/K,E)} in terms of the underlying arithmetic structure of G and certain values of zeta-functions. These results rely on the work of Arakawa (Automorphic Forms of Several Variables:
Taniguchi Symposium, Katata, 1983, eds. I. Satake and Y. Morita (Birkh?user, Boston), pp. 1–48, 1984). 相似文献
18.
H. Karami S. M. Sheikholeslami Abdollah Khodkar Douglas B. West 《Graphs and Combinatorics》2012,28(1):123-131
A set S of vertices in a graph G is a connected dominating set if every vertex not in S is adjacent to some vertex in S and the subgraph induced by S is connected. The connected domination number
γ
c
(G) is the minimum size of such a set. Let d*(G)=min{d(G),d([`(G)])}{\delta^*(G)={\rm min}\{\delta(G),\delta({\overline{G}})\}} , where [`(G)]{{\overline{G}}} is the complement of G and δ(G) is the minimum vertex degree. We prove that when G and [`(G)]{{\overline{G}}} are both connected, gc(G)+gc([`(G)]) £ d*(G)+4-(gc(G)-3)(gc([`(G)])-3){{\gamma_c}(G)+{\gamma_c}({\overline{G}})\le \delta^*(G)+4-({\gamma_c}(G)-3)({\gamma_c}({\overline{G}})-3)} . As a corollary,
gc(G)+gc([`(G)]) £ \frac3n4{{\gamma_c}(G)+{\gamma_c}({\overline{G}})\le \frac{3n}{4}} when δ*(G) ≥ 3 and n ≥ 14, where G has n vertices. We also prove that gc(G)+gc([`(G)]) £ d*(G)+2{{\gamma_c}(G)+{\gamma_c}({\overline{G}})\le \delta^*(G)+2} when gc(G),gc([`(G)]) 3 4{{\gamma_c}(G),{\gamma_c}({\overline{G}})\ge 4} . This bound is sharp when δ*(G) = 6, and equality can only hold when δ*(G) = 6. Finally, we prove that gc(G)gc([`(G)]) £ 2n-4{{\gamma_c}(G){\gamma_c}({\overline{G}})\le 2n-4} when n ≥ 7, with equality only for paths and cycles. 相似文献
19.
L. Losonczi 《Aequationes Mathematicae》1999,58(3):223-241
Summary. Let F, Y \Phi, \Psi be strictly monotonic continuous functions, F,G be positive functions on an interval I and let n ? \Bbb N \{1} n \in {\Bbb N} \setminus \{1\} . The functional equation¶¶F-1 ([(?i=1nF(xi)F(xi))/(?i=1n F(xi)]) Y-1 ([(?i=1nY(xi)G(xi))/(?i=1n G(xi))]) (x1,?,xn ? I) \Phi^{-1}\,\left({\sum\limits_{i=1}^{n}\Phi(x_{i})F(x_{i})\over\sum\limits_{i=1}^{n} F(x_{i}}\right) \Psi^{-1}\,\left({\sum\limits_{i=1}^{n}\Psi(x_{i})G(x_{i})\over\sum\limits_{i=1}^{n} G(x_{i})}\right)\,\,(x_{1},\ldots,x_{n} \in I) ¶was solved by Bajraktarevi' [3] for a fixed n 3 3 n\ge 3 . Assuming that the functions involved are twice differentiable he proved that the above functional equation holds if and only if¶¶Y(x) = [(aF(x) + b)/(cF(x) + d)], G(x) = kF(x)(cF(x) + d) \Psi(x) = {a\Phi(x)\,+\,b\over c\Phi(x)\,+\,d},\qquad G(x) = kF(x)(c\Phi(x) + d) ¶where a,b,c,d,k are arbitrary constants with k(c2+d2)(ad-bc) 1 0 k(c^2+d^2)(ad-bc)\ne 0 . Supposing the functional equation for all n = 2,3,... n = 2,3,\dots Aczél and Daróczy [2] obtained the same result without differentiability conditions.¶The case of fixed n = 2 is, as in many similar problems, much more difficult and allows considerably more solutions. Here we assume only that the same functional equation is satisfied for n = 2 and solve it under the supposition that the functions involved are six times differentiable. Our main tool is the deduction of a sixth order differential equation for the function j = F°Y-1 \varphi = \Phi\circ\Psi^{-1} . We get 32 new families of solutions. 相似文献
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