共查询到20条相似文献,搜索用时 890 毫秒
1.
We prove that, ifA is a complex Banach algebra with a unit 1 and a conjugate-linear vector space involution* such that 1*=1 and‖a
*a‖=‖a*‖ ‖a‖ for alla inA, and ifdim(A)≥3, thenA is a C*-algebra. The two-dimensional case is also considered and described. 相似文献
2.
Pascale Vitse 《Rendiconti del Circolo Matematico di Palermo》2004,53(2):283-312
For Banach space operatorsT satisfying the Tadmor-Ritt condition ‖(zI−T)−1‖≤C|z−1|−1, |z|>1, we show how to use the Riesz turndown collar theorem to estimate sup
n≥0‖T
n‖. A similar estimate is shown for lim sup
n
‖T
n‖ in terms of the Ritt constantM=lim sup
z→1‖(1−z)(zI−T)−1‖. We also obtain an estimate of the functional calculus for these operators proving, in particular, that ‖f(T)‖≤C
q‖f‖
Mult
, where ‖·‖
Mult
stands for the multiplier norm of the Cauchy-Stieltjes integrals over a Lusin type cone domain depending onC and a parameterq, 0<q<1.
Notation.D denotes the open unit disc of the complex plane,D={z∈ℂ:|z|<1}, andT={z∈ℂ:|z|=1} is the unit circle.H
∞ is the Banach algebra of bounded analytic functions onD equipped with the supremum norm ‖.‖∞. 相似文献
3.
The bicompletion of an asymmetric normed linear space 总被引:5,自引:0,他引:5
A biBanach space is an asymmetric normed linear space (X,‖·‖) such that the normed linear space (X,‖·‖s) is a Banach space, where ‖x‖s= max {‖x‖,‖-x‖} for all x∈X. We prove that each asymmetric normed linear space (X,‖·‖) is isometrically isomorphic to a dense subspace of a biBanach space (Y,‖·‖Y). Furthermore the space (Y,‖·‖Y) is unique (up to isometric isomorphism).
This revised version was published online in August 2006 with corrections to the Cover Date. 相似文献
4.
Wenjing ZHAO 《数学年刊B辑(英文版)》2011,32(2):215-222
The Cauchy problem to the Oldroyd-B model is studied. In particular, it is shown that if the smooth solution (u, τ) to this system blows up at a finite time T*, then ∫0
T* ‖▿u(t)‖
L
∞dt = ∞. Furthermore, the global existence of smooth solution to this system is given with small initial data. 相似文献
5.
In the article [2] Ennio De Giorgi conjectured that any compact n-dimensional regular submanifold M of ℝ
n+m
,moving by the gradient of the functional
where ηM is the square of the distance function from the submanifold M and Hn is the n-dimensional Hausdorff measure in ℝ n+m, does not develop singularities in finite time provided k is large enough, depending on the dimension n.
We prove this conjecture by means of the analysis of the geometric properties of the high derivatives of the distance function
from a submanifold of the Euclidean space. In particular, we show some relations with the second fundamental form and its
covariant derivatives of independent interest. 相似文献
6.
M. Zippin 《Israel Journal of Mathematics》1981,39(4):349-358
It is proved that there exists a positive function Φ(∈) defined for sufficiently small ∈ 〉 0 and satisfying limt→0 Φ(∈) =0 such that for any integersn 〉>0, ifQ is a projection ofl
1
n
onto ak-dimensional subspaceE with ‖|Q‖|≦1+∈ then there is an integerh〉=k(1−Φ(∈)) and anh-dimensional subspaceF ofE withd(F,l
1
h
) 〈= 1+Φ (∈) whered(X, Y) denotes the Banach-Mazur distance between the Banach spacesX andY. Moreover, there is a projectionP ofl
1
n
ontoF with ‖|P‖| ≦1+Φ(∈).
Author was partially supported by the N.S.F. Grant MCS 79-03042. 相似文献
7.
Jean-René Licois 《Journal d'Analyse Mathématique》1995,66(1):1-36
LetM be a compact riemannian manifold,h an odd function such thath(r)/r is non-decreasing with limit 0 at 0. Letf(r)=h(r)-γr and assume there exist non-negative constantsA andB and a realp>1 such thatf(r)>Ar
P-B. We prove that any non-negative solutionu ofu
tt+Δgu=f(u) onM x ℝ+ satisfying Dirichlet or Neumann boundary conditions on ϖM converges to a (stationary) solution of Δ
g
Φ=f(Φ) onM with exponential decay of ‖u-Φ‖C
2(M). For solutions with non-constant sign, we prove an homogenisation result for sufficiently small λ; further, we show that
for every λ the map (u(0,·),u
t(0,·))→(u(t,·), u
t(t,·)) defines a dynamical system onW
1/2(M)⊂C(M)×L
2(M) which possesses a compact maximal attractor.
相似文献
8.
Gerd Grubb 《Israel Journal of Mathematics》1971,10(1):32-95
The paper treats coerciveness inequalities (of the form Re(Au, u)≧c ‖u‖
s
2
−λ ‖u‖
0
2
,c>0,λ ∈ R) and semiboundedness inequalities (of the form Re (Au, u)≧−λ ‖u‖2) for the general boundary problems associated with an elliptic 2m-order differential operatorA in a compactn-dimensional manifold with boundary. In particular, we study the normal pseudo-differential boundary conditions, for which
we determine necessary and sufficient conditions for coerciveness withs=m, and for semiboundedness with ‖u‖ = ‖u‖m, in explicit form. 相似文献
9.
In this paper, we study the perturbation bounds for the polar decomposition A= QH where Q is unitary and H is Hermitian. The optimal (asymptotic) bounds obtained in previous works for the unitary factor, the Hermitian factor and singular values of A are σ2r||△Q||2F ≤ ||△A||2F,1/2||△H||2F ≤ ||△A||2F and ||△∑||2F ≤ ||△A||2F, respectively, where ∑ = diag(σ1, σ2,..., σr, 0,..., 0) is the singular value matrix of A and σr denotes the smallest nonzero singular value. Here we present some new combined (asymptotic)perturbation bounds σ2r ||△Q||2F 1/2||△H||2F≤ ||△A||2F and σ2r||△Q||2F ||△∑ ||2F ≤||△A||2F which are optimal for each factor. Some corresponding absolute perturbation bounds are also given. 相似文献
10.
A. Belleni-Morante 《Annali di Matematica Pura ed Applicata》1976,108(1):85-95
Riassunto. Si studia un problema non lineare di trasporto di neutroni in un muro omogeneo con sezioni d'urto dipendenti dalla temperatura.
Facendo uso di alcune tecniche standard della teoria delle equazioni non lineari di evoluzione, si prova l'esistenza e l'unicità
di una soluzione forte u=u(t), per ogni t ∈ [0,
], ove
è scelto in modo opportuno. Infine, si indica un procedimento per determinare una funzione continua e non negativa b=b(t),
tale che ‖u(t)‖⩽b(t) per ogni t ∈ [0,
].
A Dario Graffi nel suo 70o compleanno
Entrata in Redazione il 15 marzo 1975. 相似文献
Summary We study a non-linear neutron transport problem in a homogeneous slab with temperature feedback. By using some standard techniques from the theory of non-linear evolution equations, we prove existence and uniqueness of a strong solution u=u(t) at any t ∈ [0, ]. Finally, we indicate a procedure to find a non-negative continuous b=b(t), such that ‖u(t)‖⩽b(t), at any t ∈ [0, ].
A Dario Graffi nel suo 70o compleanno
Entrata in Redazione il 15 marzo 1975. 相似文献
11.
P. J. Mangheni 《Israel Journal of Mathematics》1984,48(4):341-347
LetE be a 1-injective Banach lattice,X any Banach space andT: E ← X a norm bounded linear operator. Then eitherT is an isomorphism on some copy ofl
∞ inE or for all σ > 0 there is φ ∈E
+
′
such that ‖Tu‖≦φ (|u|)+σ ‖u‖ for allu ∈E. We deduce the theorem that: A norm order continuous injective Banach lattice is order isomorphic to an (AL)-space. 相似文献
12.
David Gilat 《Israel Journal of Mathematics》1988,63(3):270-280
For eachp>1, the supremum,S, of the absolute value of a martingale terminating at a random variableX inL
p, satisfiesES≦(Γ(q))1/q‖X‖p (q=p(p-1)-1).The maximum,M, of a mean-zero martingale which starts at zero and terminates atX, satisfiesES≦(Γ(q))1/q‖X‖p (q=p(p-1)-1), whereσ
q is the unique solution of the equationt = ‖Z −t ‖
q
for an exponentially distributed random variableZ with mean 1.σ
p has other characterizations and satisfies lim
p‖
q
− 1
σ
q =c withc determined byce
c+1 = 1. Equalities in (1) and (2) are attainable by appropriate martingales which can be realized as stopped segments of Brownian
motion. A presumably new property of the exponential distribution is obtained en route to inequality (2). 相似文献
13.
J. J. Grobler 《Israel Journal of Mathematics》1988,64(1):32-38
LetA be a unital Banach lattice algebra and leta εA
+ satisfy ‖a ‖≦1. Then either ‖a
n+1 −a
n ‖=2 for alln≧0 or else ‖a
n+1 −a
n ‖ → 0 asn → ∞. Cyclicity of the peripheral spectrum ofa is also established. 相似文献
14.
Camillo De Lellis Stefan Müller 《Calculus of Variations and Partial Differential Equations》2006,26(3):283-296
Let Σ ⊂ R
3 be a smooth compact connected surface without boundary. Denote by A its second fundamental form and by Å the tensor A−(tr A/2)Id. In [4] we proved that, if ‖Å‖
L
2 (Σ) is small, then Σ is W
2,2-close to a round sphere. In this note we show that, in addition, the metric of Σ is C
0–close to the standard metric of S
2.The first author was supported by a grant of the Swiss National Science Foundation. 相似文献
15.
张正杰 《应用数学学报(英文版)》2001,17(1):47-52
1. Introduction and Main ResultIn this paper, we consider the echtence of solutions for the following equation:where g(x) 2 0, g(x)' 0, g(x) E H--'(R') andThe homogeneous case, i.e. g(x) H 0 which means zero is a trivial solution of (1.1), itwas introduced in physics. Usually it appears to be a prototype of the so-called nolilocalproblems which arise in many situations[1'2]. Many authors have proved that these equationsat least possess one positive solutionl3--sl.As we know, there is a few … 相似文献
16.
Y. Gordon 《Israel Journal of Mathematics》1970,8(4):391-397
IfX, Y are compact countable metric spaces such thatY contains no subset homeomorphic toX, then for any isomorphismΦ ofC(X) intoC(Y), ‖ φ ‖ ‖ φ−1 ‖≧3. This result and some variants of it are established here, and prove a special case of a conjecture raised in [1].
This is a part of the author’s Ph.D. Thesis prepared at the Hebrew University of Jerusalem, under the supervision of Prof.
J. Lindenstrauss. I wish to thank Prof. Lindenstrauss and Prof. A. Dvoretzky for their guidance and the interest they showed
in this work. 相似文献
17.
Alain Haraux 《Journal d'Analyse Mathématique》2005,95(1):297-321
IfA=A
*≥0 on the real Hilbert spaceH=L
2
(Ω, dμ) withKerA=A
−1
({0})∈0, (I+A)−1 compact andf(u)=c|u|
p−1
u withc>0,p>1, the solutions ofu”+u’+Au+f(u)=0 tend to 0 in norm at least liket
−1/(p−1)
ast→∞. Here it is shown that the set of initial data of those solutions tending to 0 exponentially fast has near 0 the structure
of a manifold with codimension dim(Ker A). If, in addition,A=−Δ with Neumann homogeneous boundary conditions, we show that the following alternative holds true: eitheru(t) tends to 0 exponentially fast, or ‖u(t)‖≥γt
−1/(p−1) with γ>0 fort≥1. 相似文献
18.
G. S. Watson 《Annals of the Institute of Statistical Mathematics》1986,38(1):263-275
Summary We consider distributions with densities of the formf(μ′x) andf(‖x
v
‖) where μ andx are unit vectors inR
q
and ‖x
v
‖ is the norm of the part ofx in somes dimensional subspaceV ofR
q
. For several loss functions, optimal Bayesian and Pitman estimators of μ andV are given. When uniform priors are used, these estimators are identical. Then the infinitesimal robustness characteristics
of several special cases of these estimators are calculated. 相似文献
19.
A. A. Borisenko 《Mathematical Notes》1996,60(1):3-7
In this paper we consider compact multidimensional surfaces of nonpositive external curvature in a Riemannian space. If the
curvature of the underlying space is ≥ 1 and the curvature of the surface is ≤ 1, then in small codimension the surface is
a totally geodesic submanifold that is locally isometric to the sphere. Under stricter restrictions on the curvature of the
underlying space, the submanifold is globally isometric to the unit sphere.
Translated fromMatematicheskie Zametki, Vol. 60, No. 1, pp. 3–10, July, 1996. 相似文献
20.
Roger D. Nussbaum 《Israel Journal of Mathematics》1991,76(3):345-380
Suppose thatE is a finite-dimensional Banach space with a polyhedral norm ‖·‖, i.e., a norm such that the unit ball inE is a polyhedron. ℝ
n
with the sup norm or ℝ
n
with thel
1-norm are important examples. IfD is a bounded set inE andT:D→D is a map such that ‖T(y)−T(z)‖≤ ‖y−z‖ for ally andz inE, thenT is called nonexpansive with respect to ‖·‖, and it is known that for eachx ∈D there is an integerp=p(x) such that lim
j→∞
T
jp
(x) exists. Furthermore, there exists an integerN, depending only on the dimension ofE and the polyhedral norm onE, such thatp(x)≤N: see [1,12,18,19] and the references to the literature there. In [15], Scheutzow has raised a question about the optimal
choice ofN whenE=ℝ
n
,D=K
n
, the set of nonnegative vectors in ℝ
n
, and the norm is thel
1-norm. We provide here a reasonably sharp answer to Scheutzow’s question, and in fact we provide a systematic way to generate
examples and use this approach to prove that our estimates are optimal forn≤24. See Theorem 2.1, Table 2.1 and the examples in Section 3. As we show in Corollary 2.3, these results also provide information
about the caseD=ℝ
n
, i.e.,T:ℝ
n
→ℝ
n
isl
1-nonexpansive. In addition, it is conjectured in [12] thatN=2
n
whenE=ℝ
n
and the norm is the sup norm, and such a result is optimal, if true. Our theorems here show that a sharper result is true
for an important subclass of nonexpansive mapsT:(ℝ
n
,‖ · ‖∞)→(ℝ
n
,‖ · ‖∞).
Partially supported by NSF DMS89-03018. 相似文献