共查询到20条相似文献,搜索用时 578 毫秒
1.
Jonathan Arazy 《Israel Journal of Mathematics》1975,22(3-4):247-256
Theorem.Let 1≦p≦∞,p ≠ 2, and let V be an isometry of Cp onto itself. Then there exist two unitary operators u and w on l2 so that V acts on Cp in one of the following forms: \((i) Vx = u \cdot x \cdot w; (ii) Vx = u \cdot x^T \cdot w\) (where xT is the transpose of x). 相似文献
2.
D. Somasundaram 《Proceedings Mathematical Sciences》1970,72(1):36-41
In this paper, the linear isometry of the sequence space l(pv) into itself is specified as the automorphism of l(pv) onto itself, when (pv) satisfies the conditions, (i) 0 < pv? 1, (ii) 1 +d ? pv ? p < ∞,q < qv < 1+d/d,d > o When (pv) satisfies condition (ii),l (pv) andl (qv) are proved to be perfect spaces in the sense of Kothe and Toeplitz. A similar result connecting linear isometry and automorphism has been noted in the case of a non-normable complete linear metric space whose conjugate space is also determined. 相似文献
3.
G. Schechtman 《Israel Journal of Mathematics》1975,20(3-4):351-358
It is proved that every infinite dimensional complemented subspace of (l 2⊕l 2⊕…) p (1<p<∞) with an unconditional basis is isomorphic to one of the following four spaces:l 2,l p,l 2⊕l p, (l 2⊕l 2⊕…) p . 相似文献
4.
G. Griffith Elder 《Archiv der Mathematik》2010,94(1):43-47
Let K be a complete local field of characteristic p with perfect residue field, and let L/K be a finite, totally ramified, Galois p-extension with G = Gal(L/K). Let v L be the normalized valuation with ${v_L(L^{\times})=\mathbb{Z} }Let K be a complete local field of characteristic p with perfect residue field, and let L/K be a finite, totally ramified, Galois p-extension with G = Gal(L/K). Let v
L
be the normalized valuation with
vL(L×)=\mathbbZ {v_L(L^{\times})=\mathbb{Z} }. Let pL ? L{\pi_L\in L} be a prime element, and let p′ (x) be the derivative of the minimal polynomial for π
L
over K. We show that any element r ? L{\rho\in L} with vL(r) o -vL(p¢(pL))-1 mod [L:K]{v_L(\rho)\equiv -v_L(p'(\pi_L))-1\bmod[L:K]} generates a normal basis: K[G]ρ = L. This criterion is tight: Given any integer i with
i\not o -vL(p¢(pL))-1 mod [L:K]{i\not\equiv -v_L(p'(\pi_L))-1\bmod[L:K]}, there is a ri ? L{\rho_i\in L} with v
L
(ρ
i
) = i such that
K[G]ri\subsetneq L{K[G]\rho_i\subsetneq L}. 相似文献
5.
Let {e n} be the unit vector basis ofl p, l<p<∞, and letx n=anen?bnen+1. Necessary and sufficient conditions are given for the operatorT:l p → span {x n} defined byTe i=xi to be invertible. 相似文献
6.
J. Bastero 《Archiv der Mathematik》1983,40(1):538-544
Each infinite dimensional subspace ofL p (0<p≦1) is shown to contain a copy of somel q p≦q<∞, using arguments similar to the ones that appearin Krivine and Maurey's paper concerning stable Banach spaces. Generally speaking, ifX is a stable infinite dimensionalp-Banach space, with 0<p≦1, then, there exists aq(p≦q<∞), such that,X contains (1+ε)-isomorphic copies ofl q , for all ε>0. Moreover, it is possible to prove that if a stablep-Banach space, 0<p≦1, contains an isomorphic copy ofl q,p≦q<∞, then, it also contains (1+ε) -isomorphic copies ofl q , for all ε>0. 相似文献
7.
G. V. Radzievskii 《Ukrainian Mathematical Journal》1996,48(11):1739-1757
We consider the followingK-functional: $$K(\delta ,f)_p : = \mathop {\sup }\limits_{g \in W_{p U}^r } \left\{ {\left\| {f - g} \right\|_{L_p } + \delta \sum\limits_{j = 0}^r {\left\| {g^{(j)} } \right\|_{L_p } } } \right\}, \delta \geqslant 0,$$ where ? ∈L p :=L p [0, 1] andW p,U r is a subspace of the Sobolev spaceW p r [0, 1], 1≤p≤∞, which consists of functionsg such that $\int_0^1 {g^{(l_j )} (\tau ) d\sigma _j (\tau ) = 0, j = 1, ... , n} $ . Assume that 0≤l l ≤...≤l n ≤r-1 and there is at least one point τ j of jump for each function σ j , and if τ j =τ s forj ≠s, thenl j ≠l s . Let $\hat f(t) = f(t)$ , 0≤t≤1, let $\hat f(t) = 0$ ,t<0, and let the modulus of continuity of the functionf be given by the equality $$\hat \omega _0^{[l]} (\delta ,f)_p : = \mathop {\sup }\limits_{0 \leqslant h \leqslant \delta } \left\| {\sum\limits_{j = 0}^l {( - 1)^j \left( \begin{gathered} l \hfill \\ j \hfill \\ \end{gathered} \right)\hat f( - hj)} } \right\|_{L_p } , \delta \geqslant 0.$$ We obtain the estimates $K(\delta ^r ,f)_p \leqslant c\hat \omega _0^{[l_1 ]} (\delta ,f)_p $ and $K(\delta ^r ,f)_p \leqslant c\hat \omega _0^{[l_1 + 1]} (\delta ^\beta ,f)_p $ , where β=(pl l + 1)/p(l 1 + 1), and the constantc>0 does not depend on δ>0 and ? ∈L p . We also establish some other estimates for the consideredK-functional. 相似文献
8.
Dumitru Popa 《Archiv der Mathematik》2014,103(3):291-300
We use the Maurey–Rosenthal factorization theorem to give a characterization of almost summing and multiple almost summing multilinear operators on a cartesian product of l p spaces. As applications we give the necessary and sufficient conditions for the multiplication operator on l p spaces be almost summing and multiple almost summing. 相似文献
9.
10.
P. K. Chaurasia 《Analysis Mathematica》2009,35(1):15-35
Let G denote a locally compact abelian group and H a separable Hilbert space. Let L p (G, H), 1 ≤ p < ∞, be the space of H-valued measurable functions which are in the usual L p space. Motivated by the work of Helgason [1], Figa-Talamanca [11] and Bachelis [2, 3], we have defined the derived space of the Banach space L p (G, H) and have studied its properties. Similar to the scalar case, we prove that if G is a noncompact, locally compact abelian group, then L p 0 (G, H) = {0} holds for 1 ≤ p < 2. Let G be a compact abelian group and Γ be its dual group. Let S p (G, H) be the L 1(G) Banach module of functions in L p (G, H) having unconditionally convergent Fourier series in L p -norm. We show that S p (G, H) coincides with the derived space L p 0 (G, H), as in the scalar valued case. We also show that if G is compact and abelian, then L p 0 (G, H) = L 2(G, H) holds for 1 ≤ p ≤ 2. Thus, if F ∈ L p (G, H), 1 ≤ p < 2 and F has an unconditionally convergent Fourier series in L p -norm, then F ∈ L 2(G, H). Let Ω be the set of all functions on Γ taking only the values 1, ?1 and Ω* be the set of all complex-valued functions on Γ having absolute value 1. As an application of the derived space L p 0 (G, H), we prove the following main result of this paper. Let G be a compact abelian group and F be an H-valued function on the dual group Γ such that $$ \sum \omega (\gamma )F(\gamma )\gamma $$ is a Fourier-Stieltjes series of some measure µ ∈ M(G, H) for every scalar function ω such that |ω(γ)| = 1. Then F ∈ l 2(Γ, H). 相似文献
11.
12.
We study a family of topologies {s}0 on the space lp, 0 is the protective topology on lp generated by the family of multipliers my:lpls, my(x)=x · y, where y ranges over the space lp and 1/p + 1/q=1/s. Here ls is taken with its standard topology generated by the norm for s 1 or a pseudonorm if 0s}0sp is strictly increasing and that all the topologies s, 0s are not locally convex when 0Matematicheskie Metody i Fiziko-Mekhanicheskie Polya, Issue 35, 1992, pp. 194–198. 相似文献
s
13.
The conjecture that every Banach space contains uniformly complementedl p n ’s for some 1≦p≦∞ is verified for subspaces of Banach lattices which do not containl ∞ n ’s uniformly. 相似文献
14.
Tay-Woei Shyu 《Graphs and Combinatorics》2013,29(2):301-313
Let C k denote a cycle of length k and let S k denote a star with k edges. As usual K n denotes the complete graph on n vertices. In this paper we investigate decomposition of K n into C l ’s and S k ’s, and give some necessary or sufficient conditions for such a decomposition to exist. In particular, we give a complete solution to the problem in the case l = k = 4 as follows: For any nonnegative integers p and q and any positive integer n, there exists a decomposition of K n into p copies of C 4 and q copies of S 4 if and only if ${4(p + q)={n \choose 2}, q\ne 1}$ if n is odd, and ${q\geq max\{3, \lceil{\frac{n}{4}\rceil}\}}$ if n is even. 相似文献
15.
Let E=Lp or lp space, 1<p<∞. Let K be a closed, convex and nonempty subset of E. Let be a family of nonexpansive self-mappings of K. For arbitrary fixed δ∈(0,1), define a family of nonexpansive maps by Si?(1−δ)I+δTi where I is the identity map of K. Let . It is proved that the iterative sequence {xn} defined by: x0∈K,xn+1=αnu+∑i≥1σi,tnSixn,n≥0 converges strongly to a common fixed point of the family where {αn} and {σi,tn} are sequences in (0,1) satisfying appropriate conditions, in each of the following cases: (a) E=lp,1<p<∞, and (b) E=Lp,1<p<∞ and at least one of the maps Ti’s is demicompact. Our theorems extend the results of [P. Maingé, Approximation methods for common fixed points of nonexpansive mappings in Hilbert space, J. Math. Anal. Appl. 325 (2007) 469-479] from Hilbert spaces to lp spaces, 1<p<∞. 相似文献
16.
V. G. Maz'ya 《Journal of Mathematical Sciences》1983,23(1):1997-2003
It is proved that for all fractionall the integral \(\int\limits_0^\infty {(p,\ell ) - cap(M_t )} dt^p\) is majorized by the P-th power norm of the functionu in the space ? p l (Rn) (here Mt={x∶¦u(x)¦?t} and (p,l)-cap(e) is the (p,l)-capacity of the compactum e?Rn). Similar results are obtained for the spaces W p l (Rn) and the spaces of M. Riesz and Bessel potentials. One considers consequences regarding imbedding theorems of “fractional” spaces in ?q(dμ), whereμ is a nonnegative measure in Rn. One considers specially the case p=1. 相似文献
17.
Soohyun Bae 《Journal of Differential Equations》2009,247(5):1616-1635
We establish that the elliptic equation Δu+K(x)up+μf(x)=0 in Rn has a continuum of positive entire solutions for small μ?0 under suitable conditions on K, p and f. In particular, K behaves like l|x| at ∞ for some l?−2, but may change sign in a compact region. For given l>−2, there is a critical exponent pc=pc(n,l)>1 in the sense that the result holds for p?pc and involves partial separation of entire solutions. The partial separation means that the set of entire solutions possesses a non-trivial subset in which any two solutions do not intersect. The observation is well known when K is non-negative. The point of the paper is to remove the sign condition on compact region. When l=−2, the result holds for any p>1 while pc is decreasing to 1 as l decreases to −2. 相似文献
18.
Let T and A be two nonnegative regular summability matrices and W(T,p)∩l∞ and cA(b) denote the spaces of all bounded strongly T-summable sequences with index p>0, and bounded summability domain of A, respectively. In this paper we show, among other things, that is a multiplier from W(T,p)∩l∞ into cA(b) if and only if any subset K of positive integers that has T-density zero implies that K has A-density zero. These results are used to characterize the A-statistical comparisons for both bounded as well as arbitrary sequences. Using the concept of A-statistical Tauberian rate, we also show that is not a multiplier from W(T,p)∩l∞ into cA(b) that leads to a Steinhaus type result. 相似文献
19.
G. A. Watson 《Numerical Algorithms》1994,8(1):135-146
Consideration is given to problems of linear best approximation using a variant of the usuall
p
norms referred to ask-majorl
p
norms, for the cases when 1<p<. The underlying problem is the minimization of a piecewise smooth function. Best approximations are characterized, and a descent algorithm is developed. 相似文献
20.
Bernard Fichet 《Advances in Data Analysis and Classification》2009,3(3):305-314
Given a frequency table ${F=\{f_{jk},(j,k)\in\,J\times K\}}$ crossing two categorical variables J and K, we consider a family of metrics of L p -type on J defined by ${d_J^p (j,j^{\prime}) = \Sigma_k g(f_{.k})|f_{jk}/f_{j.} - f_{j^{\prime}k}/f_{j^{\prime}.}|^p}$ , where g is a positive function, and a symmetrical one on K. We investigate under which conditions on g, the famous principle of distributional equivalence is fulfilled by these metrics for every rational or every real F. 相似文献