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1.
Let K be a complete ultrametric algebraically closed field and let A be the K-Banach algebra of bounded analytic functions in the disk . Let Mult(A,‖⋅‖) be the set of continuous multiplicative semi-norms of A, let Multm(A,‖⋅‖) be the subset of the ?∈Mult(A,‖⋅‖) whose kernel is a maximal ideal and let Multa(A,‖⋅‖) be the subset of the ?∈Multm(A,‖⋅‖) whose kernel is of the form (if ?∈Multm(A,‖⋅‖)?Multa(A,‖⋅‖), the kernel of ? is then of infinite codimension). The main problem we examine is whether Multa(A,‖⋅‖) is dense inside Multm(A,‖⋅‖) with respect to the topology of simple convergence. This a first step to the conjecture of density of Multa(A,‖⋅‖) in the whole set Mult(A,‖⋅‖): this is the corresponding problem to the well-known complex corona problem. We notice that if ?∈Multm(A,‖⋅‖) is defined by an ultrafilter on D, ? lies in the closure of Multa(A,‖⋅‖). Particularly, we shaw that this is case when a maximal ideal is the kernel of a unique ?∈Multm(A,‖⋅‖). Thus, if every maximal ideal is the kernel of a unique ?∈Multm(A,‖⋅‖), Multa(A,‖⋅‖) is dense in Multm(A,‖⋅‖). And particularly, this is the case when K is strongly valued. In the general context, we find a subset of Multm(A,‖⋅‖)?Multa(A,‖⋅‖) which is included in the closure of Multa(A,‖⋅‖). More generally, we show that if ψ∈Mult(A,‖⋅‖) does not define the Gauss norm on polynomials (‖⋅‖), then it is characterized by a circular filter, like on rational functions and analytic elements. As a consequence, if ψ does not lie in the closure of Multa(A,‖⋅‖), then its restriction to polynomials is the Gauss norm. 相似文献
2.
LetA
e
be the algebra obtained by adjoining identity to a non-unital Banach algebra (A, ∥ · ∥). Unlike the case for aC*-norm on a Banach *-algebra,A
e
admits exactly one uniform norm (not necessarily complete) if so doesA. This is used to show that the spectral extension property carries over fromA to A
e
. Norms onA
e
that extend the given complete norm ∥ · ∥ onA are investigated. The operator seminorm ∥ · ∥op onA
e
defined by ∥ · ∥ is a norm (resp. a complete norm) iffA has trivial left annihilator (resp. ∥ · ∥op restricted toA is equivalent to ∥ · ∥). 相似文献
3.
Xiao Jie 《数学学报(英文版)》1994,10(2):192-201
LetD={z∈Σ:|z|<1} and ϕ be a normal function on [0,1). Forp∈(0,1) such a function ϕ is used to define a Bergman spaceA
p
(ϕ) onD with weight ϕ
p
(|·|)/(1-|·|2). In this paper, the dual space ofA
p
(ϕ) is given, four characteristics of Carleson measure onA
p
(ϕ) are obtained. Moreover, as an application, three sequence interpolation theorems inA
p
(ϕ) are derived.
Supported by the Doctoral Program Foundation of Institute of Higher Education, P.R. China. 相似文献
4.
Balázs Csikós György Kiss Konrad J. Swanepoel P. Oloff de Wet 《Periodica Mathematica Hungarica》2009,58(2):129-138
A family {A
i
| i ∈ I} of sets in ℝ
d
is antipodal if for any distinct i, j ∈ I and any p ∈ A
i
, q ∈ A
j
, there is a linear functional ϕ:ℝ
d
→ ℝ such that ϕ(p) ≠ ϕ(q) and ϕ(p) ≤ ϕ(r) ≤ ϕ(q) for all r ∈ ∪
i∈I
A
i
. We study the existence of antipodal families of large finite or infinite sets in ℝ3.
The research was supported by the Hungarian-South African Intergovernmental Scientific and Technological Cooperation Programme,
NKTH Grant no. ZA-21/2006 and South African National Research Foundation Grant no. UID 61853, as well as Hungarian National
Foundation for Scientific Research Grants no. NK 67867, no. T47102, and no. K72537. 相似文献
5.
V. V. Kapustin 《Journal of Mathematical Sciences》2007,141(5):1538-1542
Let θ be an inner function, let K
θ
= H
2 ⊖ θH
2, and let Sθ : Kθ → Sθ be defined by the formula Sθf = Pθzf, where f ∈ Kθ is the orthogonal projection of H2 onto Kθ. Consider the set A of all trace class operators L : Kθ → Kθ, L = ∑(·,un)vn, ∑∥un∥∥vn∥ < ∞ (un, vn ∈ Kθ), such that ∑ūn vn ∈ H
0
1
. It is shown that trace class commutators of the form XSθ − SθX (where X is a bounded linear operator on Kθ) are dense in A in the trace class norm. Bibliography: 2 titles.
__________
Translated from Zapiski Nauchnykh Seminarov POMI, Vol. 333, 2006, pp. 54–61. 相似文献
6.
Huan Yin CHEN 《数学学报(英文版)》2007,23(2):357-364
Let R be an exchange ring with primitive factors artinian. We prove that there exists a u∈U(R) such that 1R ± u ∈ U(R), if and only if for any a ∈ R, there exists a u ∈ U(R) such that a ± u∈ U(R). Phrthermore, we prove that, for any A ∈ Mn(R)(n ≥ 2), there exists a U ∈ GLn(R) such that A ± U ∈ GLn(R). 相似文献
7.
M. F. Gamal' 《Journal of Mathematical Sciences》1998,92(1):3589-3596
Let B be a Blaschke product with simple zeros in the unit disk, let Λ be the set of its zeros, and let ϕ∈H∞. It is known that ϕ+BH∞ is a weak* generator of the algebra H∞/BH∞ if (for B that satisfy the Carleson condition (C)) and only if the sequence ϕ(Λ) is a weak* generator of the algebra l∞. In this paper, we show that for any Blaschke product B with simple zeros that does not satisfy condition (C), there exists
B=B1·…·BN, where N ∈ℕ, and B1, …, BN are Blaschke products satisfying condition (C), there exists a function ϕ∈H∞ such that ϕ(Λ) is a weak* generator of the algebra l∞, and ϕ+BH∞ is not a weak* generator of the algebra H∞/BH∞. Bibliography: 12 titles.
Translated fromZapiski Nauchnykh Seminarov POMI, Vol. 232, 1996, pp. 73–85.
Translated by M. F. Gamal'. 相似文献
8.
A. Escassut 《P-Adic Numbers, Ultrametric Analysis, and Applications》2016,8(2):115-124
Let IK be a complete ultrametric algebraically closed field and let A be the Banach IK-algebra of bounded analytic functions in the ”open” unit disk D of IK provided with the Gauss norm. Let Mult(A, ‖. ‖) be the set of continuous multiplicative semi-norms of A provided with the topology of simple convergence, let Mult m (A, ‖. ‖) be the subset of the ? ∈ Mult(A, ‖. ‖) whose kernel is amaximal ideal and let Mult 1(A, ‖. ‖) be the subset of the ? ∈ Mult(A, ‖. ‖) whose kernel is a maximal ideal of the form (x ? a)A with a ∈ D. By analogy with the Archimedean context, one usually calls ultrametric Corona problem the question whether Mult 1(A, ‖. ‖) is dense in Mult m (A, ‖. ‖). In a previous paper, it was proved that when IK is spherically complete, the answer is yes. Here we generalize this result to any algebraically closed complete ultrametric field, which particularly applies to ? p . On the other hand, we also show that the continuous multiplicative seminorms whose kernel are neither a maximal ideal nor the zero ideal, found by Jesus Araujo, also lie in the closure of Mult 1(A, ‖. ‖), which suggest that Mult 1(A, ‖. ‖)might be dense in Mult(A, ‖. ‖). 相似文献
9.
Mikhail A. Chebotar Wen-Fong Ke Pjek-Hwee Lee Ruibin Zhang 《Monatshefte für Mathematik》2006,162(1):91-101
Let R be a ring, A = M
n
(R) and θ: A → A a surjective additive map preserving zero Jordan products, i.e. if x,y ∈ A are such that xy + yx = 0, then θ(x)θ(y) + θ(y)θ(x) = 0. In this paper, we show that if R contains
\frac12\frac{1}{2}
and n ≥ 4, then θ = λϕ, where λ = θ(1) is a central element of A and ϕ: A → A is a Jordan homomorphism. 相似文献
10.
Abstract
The singular second-order m-point boundary value problem
, is considered under some conditions concerning the first eigenvalue of the relevant linear operators, where (Lϕ)(x) = (p(x)ϕ′(x))′ + q(x)ϕ(x) and ξ
i
∈ (0, 1) with 0 < ξ1 < ξ2 < · · · < ξ
m−2 < 1, a
i
∈ [0, ∞). h(x) is allowed to be singular at x = 0 and x = 1. The existence of positive solutions is obtained by means of fixed point index theory. Similar conclusions hold for some
other m-point boundary value conditions.
Supported by the National Natural Science Foundation of China (No.10371066, No.10371013) 相似文献
11.
Vikram K. Srimurthy 《Probability Theory and Related Fields》2000,118(4):522-546
Let K be a simply-connected compact Lie Group equipped with an Ad
K
-invariant inner product on the Lie Algebra ?, of K. Given this data, there is a well known left invariant “H
1-Riemannian structure” on L(K) (the infinite dimensional group of continuous based loops in K), as well as a heat kernel νT(k
0, ·) associated with the Laplace-Beltrami operator on L(K). Here T > 0, k
0∈L(K), and ν
T
(k
0, ·) is a certain probability measure on L(K). In this paper we show that ν1(e,·) is equivalent to Pinned Wiener Measure on K on ?
s0
≡<x
t
: t∈ [0, s
0]> (the σ-algebra generated by truncated loops up to “time”s
0).
Recevied: 9 September 1999 / Revised version: 13 March 2000 / Published online: 22 November 2000 相似文献
12.
Mikhail A. Chebotar Wen-Fong Ke Pjek-Hwee Lee Ruibin Zhang 《Monatshefte für Mathematik》2006,149(2):91-101
Let R be a ring, A = M
n
(R) and θ: A → A a surjective additive map preserving zero Jordan products, i.e. if x,y ∈ A are such that xy + yx = 0, then θ(x)θ(y) + θ(y)θ(x) = 0. In this paper, we show that if R contains
and n ≥ 4, then θ = λϕ, where λ = θ(1) is a central element of A and ϕ: A → A is a Jordan homomorphism.
The third author is Corresponding author. 相似文献
13.
Two operators A, B ∈ B(H) are said to be strongly approximatively similar, denoted by A -sas B, if (i) given ε 〉 0, there exist Ki ∈ B(H) compact with ||Ki|| 〈ε(i = 1,2) such that A+K1 and B + K2 are similar; (ii) σ0(A) = σ0(B) and dim H(λ; A) = dim H(λ; B) for each λ ∈ σ0(A). In this paper, we prove the following result. Let S,T ∈ B(H) be quasitriangular satisfying: (i) σ(T) = σ(S) = σw(S) is connected and σe(S) = σlre(S); (ii) ρs-F(S) ∩ σ(S) consists of at most finite components and each component Ω satisfies that Ω = int Ω, where int Ω is the interior of Ω. Then, S -sas T if and only if S and T are essentially similar. 相似文献
14.
Liangping Jiang 《Journal of Mathematical Sciences》2011,177(3):395-401
The classical criterion of asymptotic stability of the zero solution of equations x′ = f(t, x) is that there exists a function V (t, x), a(∥x∥) ≤ V (t, x) ≤ b(∥x∥) for some a, b ∈ K such that [(V)\dot] \dot{V} (t, x) ≤ −c(∥x∥) for some c ∈ K. In this paper, we prove that if V(m + 1) \mathop {V}\limits^{(m + {1})} (t, x) is bounded on some set [tk − T, tk + T] × BH(tk → +∞ as k → ∞), then the condition that [(V)\dot] \dot{V} (t, x) ≤ −c(∥x∥) can be weakened and replaced by that [(V)\dot] \dot{V} (t, x) ≤ 0 and − (−[(V)\dot] \dot{V} (tk, x)| + − [(V)\ddot] \ddot{V} (tk, x)| + ⋯ + − V(m) \mathop {V}\limits^{(m)} (tk, x)|) ≤ −c′(∥x∥) for some c′ ∈ K. Moreover, the author also presents a corresponding instability criterion. [1–10] 相似文献
15.
Clustering of linearly interacting diffusions and universality of their long-time limit distribution
J. M. Swart 《Probability Theory and Related Fields》2000,118(4):574-594
Let K⊂ℝ
d
(d≥ 1) be a compact convex set and Λ a countable Abelian group. We study a stochastic process X in K
Λ, equipped with the product topology, where each coordinate solves a SDE of the form dX
i
(t) = ∑
j
a(j−i) (X
j
(t) −X
i
(t))dt + σ (X
i
(t))dB
i
(t). Here a(·) is the kernel of a continuous-time random walk on Λ and σ is a continuous root of a diffusion matrix w on K. If X(t) converges in distribution to a limit X(∞) and the symmetrized random walk with kernel a
S
(i) = a(i) + a(−i) is recurrent, then each component X
i
(∞) is concentrated on {x∈K : σ(x) = 0 and the coordinates agree, i.e., the system clusters. Both these statements fail if a
S
is transient. Under the assumption that the class of harmonic functions of the diffusion matrix w is preserved under linear transformations of K, we show that the system clusters for all spatially ergodic initial conditions and we determine the limit distribution of
the components. This distribution turns out to be universal in all recurrent kernels a
S
on Abelian groups Λ.
Received: 10 May 1999 / Revised version: 18 April 2000 / Published online: 22 November 2000 相似文献
16.
Osamu Hatori Takeshi Miura Rumi Shindo Hiroyuki Takagi 《Rendiconti del Circolo Matematico di Palermo》2010,59(2):161-183
Let $
A
$
A
and ℬ be unital semisimple commutative Banach algebras. It is shown that if surjections S,T: $
A
$
A
→ ℬ with S(1)=T(1)= 1 and α ∈ ℂ \ {0} satisfy r(S(a)T(b) − α)= r(ab− α) for all a,b ∈ $
A
$
A
, then S=T and S is a real algebra isomorphism, where r(a) is the spectral radius of a. Let I be a nonempty set, A and B be uniform algebras. Let ρ, τ: I → A and S,T: I → B be maps satisfying σ
π
(S(p)T(q)) ⊂ σ
π
(ρ(p) τ(q)) for all p,q ∈ I, where σ
π
(f) is the peripheral spectrum of f. Suppose that the ranges ρ(I), τ(I) ⊂ A and S(I),T(I) ⊂ B are closed under multiplication in a sense, and contain peaking functions “enough”. There exists a homeomorphism ϕ: Ch(B)→Ch(A) such that S(p)(y)= ρ(p)(ϕ(y)) and T(p)(y)= τ(p)(ϕ(y)) for every p ∈ I and y ∈ Ch(B), where Ch(A) is the Choquet boundary of A. 相似文献
17.
It is proved that all the equivalence relations of a universal algebra A are its congruences if and only if either |A| ≤ 2 or every operation f of the signature is a constant (i.e., f(a
1
, . . . , a
n
) = c for some c ∈ A and all the a
1
, . . . , a
n
∈ A) or a projection (i.e., f(a
1
, . . . , a
n
) = a
i
for some i and all the a
1
, . . . , a
n
∈ A). All the equivalence relations of a groupoid G are its right congruences if and only if either |G| ≤ 2 or every element a ∈ G is a right unit or a generalized right zero (i.e., x
a
= y
a
for all x, y ∈ G). All the equivalence relations of a semigroup S are right congruences if and only if either |S| ≤ 2 or S can be represented as S = A∪B, where A is an inflation of a right zero semigroup, and B is the empty set or a left zero semigroup, and ab = a, ba = a
2 for a ∈ A, b ∈ B. If G is a groupoid of 4 or more elements and all the equivalence relations of it are right or left congruences, then either all
the equivalence relations of the groupoid G are left congruences, or all of them are right congruences. A similar assertion for semigroups is valid without the restriction
on the number of elements. 相似文献
18.
Masahiro Yasumoto 《manuscripta mathematica》1990,66(1):227-235
LetK be an algebraic number field of finite degree andf(X,T) a polynomial overK. For eachφ(X)∈Z[X], we denote byE(φ) the set of all integersa with φ
m
(a) =φ
n
(a) for somem≠n. In this paper, we give a condition for a polynomialφ(X)∈Z[X] to satisfy the following; If forn∈N, there existr∈K anda∈Z−E(φ) such thatf r, φ
m
(a)=0, then there exists a rational functiong(X) overK andk∈N such thatf(g(T)), φ
k
(T))=0 . 相似文献
19.
Von Neumann-Jordan Constants of Absolute Normalized Norms on C^n 总被引:1,自引:0,他引:1
In this note, we give some estimations of the Von Neumann-Jordan constant C
N J
(∥·∥ψ) of Banach space (ℂ
n
, ∥·∥ψ), where ∥·∥ψ is the absolute normalized norm on ℂ
n
given by function ψ. In the case where ψ and φ are comparable, n=2 and C
N J
(∥·∥ψ)=1, we obtain a formula of computing C
N J
(∥·∥ψ). Our results generalize some results due to Saito and others.
Received May 11, 2002, Accepted November 20, 2002
This work is partly supported by NNSF of China (No. 19771056) 相似文献
20.
Let A and B be standard operator algebras on Banach spaces X and Y, respectively. The peripheral spectrum σπ (T) of T is defined by σπ (T) = z ∈ σ(T): |z| = maxw∈σ(T) |w|. If surjective (not necessarily linear nor continuous) maps φ, ϕ: A → B satisfy σπ (φ(S)ϕ(T)) = σπ (ST) for all S; T ∈ A, then φ and ϕ are either of the form φ(T) = A
1
TA
2
−1 and ϕ(T) = A
2
TA
1
−1 for some bijective bounded linear operators A
1; A
2 of X onto Y, or of the form φ(T) = B
1
T*B
2
−1 and ϕ(T) = B
2
T*B
−1 for some bijective bounded linear operators B
1;B
2 of X* onto Y.
相似文献