共查询到20条相似文献,搜索用时 24 毫秒
1.
Rumi Shindo 《Central European Journal of Mathematics》2010,8(1):135-147
Let A and B be uniform algebras. Suppose that α ≠ 0 and A
1 ⊂ A. Let ρ, τ: A
1 → A and S, T: A
1 → B be mappings. Suppose that ρ(A
1), τ(A
1) and S(A
1), T(A
1) are closed under multiplications and contain expA and expB, respectively. If ‖S(f)T(g) − α‖∞ = ‖ρ(f)τ(g) − α‖∞ for all f, g ∈ A
1, S(e
1)−1 ∈ S(A
1) and S(e
1) ∈ T(A
1) for some e
1 ∈ A
1 with ρ(e
1) = 1, then there exists a real-algebra isomorphism $
\tilde S
$
\tilde S
: A → B such that $
\tilde S
$
\tilde S
(ρ(f)) = S(e
1)−1
S(f) for every f ∈ A
1. We also give some applications of this result. 相似文献
2.
Let H be a Hilbert space and A be a standard *-subalgebra of B(H). We show that a bijective map Ф : A →A preserves the Lie-skew product AB - BA* if and only if there is a unitary or conjugate unitary operator U ∈A(H) such that Ф(A) = UAU* for all A ∈ A, that is, Фis a linear * -isomorphism or a conjugate linear *-isomorphism. 相似文献
3.
Let H be an infinite dimensional complex Hilbert space. Denote by B(H) the algebra of all bounded linear operators on H, and by I(H) the set of all idempotents in B(H). Suppose that Φ is a surjective map from B(H) onto itself. If for every λ ∈ -1,1,2,3, and A, B ∈ B(H),A-λB ∈I(H) ⇔ Φ(A) -λΦ(B) ∈I(H, then Φ is a Jordan ring automorphism, i.e. there exists a continuous invertible linear or conjugate linear operator T on H such that Φ(A) = TAT
-1 for all A ∈ B(H), or Φ(A) = TA*T
-1 for all A ∈ B(H); if, in addition, A-iB ∈I(H)⇔ Φ(A)-iΦ(B) ∈I(H), here i is the imaginary unit, then Φ is either an automorphism or an anti-automorphism. 相似文献
4.
If the second order problem u(t) + Bu(t) + Au(t) = f(t), u(0) =u(0) = 0 has L^p-maximal regularity, 1 〈 p 〈 ∞, the analyticity of the corresponding propagator of the sine type is shown by obtaining the estimates of ‖λ(λ^2 + λB + A)^-1‖ and ‖B(λ^2 + λB + A)^-1‖ for λ∈ C with Reλ 〉 ω, where the constant ω≥ 0. 相似文献
5.
Takeshi Miura 《Central European Journal of Mathematics》2011,9(4):778-788
Let A and B be uniformly closed function algebras on locally compact Hausdorff spaces with Choquet boundaries Ch A and ChB, respectively. We prove that if T: A → B is a surjective real-linear isometry, then there exist a continuous function κ: ChB → {z ∈ ℂ: |z| = 1}, a (possibly empty) closed and open subset K of ChB and a homeomorphism φ: ChB → ChA such that T(f) = κ(f ∘φ) on K and T( f ) = k[`(fof)]T\left( f \right) = \kappa \overline {fo\phi } on ChB \ K for all f ∈ A. Such a representation holds for surjective real-linear isometries between (not necessarily uniformly closed) function algebras. 相似文献
6.
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
7.
Milan Jasem 《Mathematica Slovaca》2011,61(5):827-833
Let A = (A,⊕,−,∼, 0, 1) be a GMV-algebra and ρ: A × A → A the distance function on A defined by ρ(x, y) = (x∨y)−(x∧y) for each x, y ∈ A. 相似文献
8.
Hongwei Sun 《Frontiers of Mathematics in China》2007,2(3):455-465
Let H be a Hilbert space, A ∈ L(H), y ∈
, and y ∉ R(A). We study the behavior of the distance square between y and A(B
τ), defined as a functional F(τ), as the radius τ of the ball B
τ of H tends to ∞. This problem is important in estimating the approximation error in learning theory. Our main result is to estimate
the asymptotic behavior of F(τ) without the compactness assumption on the operator A. We also consider the Peetre K-functional and its convergence rates.
相似文献
9.
Yusup Kh. Eshkabilov 《Central European Journal of Mathematics》2008,6(1):149-157
Let Ω= [a, b] × [c, d] and T
1, T
2 be partial integral operators in (Ω): (T
1
f)(x, y) =
k
1(x, s, y)f(s, y)ds, (T
2
f)(x, y) =
k
2(x, ts, y)f(t, y)dt where k
1 and k
2 are continuous functions on [a, b] × Ω and Ω × [c, d], respectively. In this paper, concepts of determinants and minors of operators E−τT
1, τ ∈ ℂ and E−τT
2, τ ∈ ℂ are introduced as continuous functions on [a, b] and [c, d], respectively. Here E is the identical operator in C(Ω). In addition, Theorems on the spectra of bounded operators T
1, T
2, and T = T
1 + T
2 are proved.
相似文献
11.
Let A and B denote two families of subsets of an n-element set. The pair (A,B) is said to be ℓ-cross-intersecting iff |A∩B|=ℓ for all A∈ A and B∈B. Denote by P
e
(n) the maximum value of |A||B| over all such pairs. The best known upper bound on P
e
(n) is Θ(2
n
), by Frankl and R?dl. For a lower bound, Ahlswede, Cai and Zhang showed, for all n ≥ 2ℓ, a simple construction of an ℓ-cross-intersecting pair (A,B) with |A||B| = $
\left( {{*{20}c}
{2\ell } \\
\ell \\
} \right)
$
\left( {\begin{array}{*{20}c}
{2\ell } \\
\ell \\
\end{array} } \right)
2
n−2ℓ
= Θ(2
n
/$
\sqrt \ell
$
\sqrt \ell
), and conjectured that this is best possible. Consequently, Sgall asked whether or not P
e
(n) decreases with ℓ. 相似文献
12.
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
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.
Let A and B be unital, semisimple commutative Banach algebras with the maximal ideal spaces M
A
and M
B
, respectively, and let r(a) be the spectral radius of a. We show that if T: A → B is a surjective mapping, not assumed to be linear, satisfying r(T(a) + T(b)) = r(a + b) for all a; b ∈ A, then there exist a homeomorphism φ: M
B
→ M
A
and a closed and open subset K of M
B
such that
$
\widehat{T\left( a \right)}\left( y \right) = \left\{ \begin{gathered}
\widehat{T\left( e \right)}\left( y \right)\hat a\left( {\phi \left( y \right)} \right) y \in K \hfill \\
\widehat{T\left( e \right)}\left( y \right)\overline {\hat a\left( {\phi \left( y \right)} \right)} y \in M_\mathcal{B} \backslash K \hfill \\
\end{gathered} \right.
$
\widehat{T\left( a \right)}\left( y \right) = \left\{ \begin{gathered}
\widehat{T\left( e \right)}\left( y \right)\hat a\left( {\phi \left( y \right)} \right) y \in K \hfill \\
\widehat{T\left( e \right)}\left( y \right)\overline {\hat a\left( {\phi \left( y \right)} \right)} y \in M_\mathcal{B} \backslash K \hfill \\
\end{gathered} \right.
相似文献
15.
Let A and B be Banach function algebras on compact Hausdorff spaces X and Y and let ‖.‖
X
and ‖.‖
Y
denote the supremum norms on X and Y, respectively. We first establish a result concerning a surjective map T between particular subsets of the uniform closures of A and B, preserving multiplicatively the norm, i.e. ‖Tf Tg‖
Y
= ‖fg‖
X
, for certain elements f and g in the domain. Then we show that if α ∈ ℂ {0} and T: A → B is a surjective, not necessarily linear, map satisfying ‖fg + α‖
X
= ‖Tf Tg + α‖
Y
, f,g ∈ A, then T is injective and there exist a homeomorphism φ: c(B) → c(A) between the Choquet boundaries of B and A, an invertible element η ∈ B with η(Y) ⊆ {1, −1} and a clopen subset K of c(B) such that for each f ∈ A,
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