共查询到20条相似文献,搜索用时 31 毫秒
1.
Ralph deLaubenfels 《Israel Journal of Mathematics》1993,81(1-2):227-255
We show that, whenA generates aC-semigroup, then there existsY such that [M(C)] →Y →X, andA|
Y
, the restriction ofA toY, generates a strongly continuous semigroup, where ↪ means “is continuously embedded in” and ‖x‖[Im(C)]≡‖C
−1
x‖. There also existsW such that [C(W)] →X →W, and an operatorB such thatA=B|
X
andB generates a strongly continuous semigroup onW. If theC-semigroup is exponentially bounded, thenY andW may be chosen to be Banach spaces; in general,Y andW are Frechet spaces. If ρ(A) is nonempty, the converse is also true.
We construct fractional powers of generators of boundedC-semigroups.
We would like to thank R. Bürger for sending preprints, and the referee for pointing out reference [37]. This research was
supported by an Ohio University Research Grant. 相似文献
2.
Fixed point theorems for non-Lipschitzian mappings of asymptotically nonexpansive type 总被引:17,自引:0,他引:17
W. A. Kirk 《Israel Journal of Mathematics》1974,17(4):339-346
LetX be a Banach space,K a nonempty, bounded, closed and convex subset ofX, and supposeT:K→K satisfies: for eachx∈K, lim sup
i→∞{sup
y∈K
‖t
ix−Tiy∼−‖x−y‖}≦0. IfT
N is continuous for some positive integerN, and if either (a)X is uniformly convex, or (b)K is compact, thenT has a fixed point inK. The former generalizes a theorem of Goebel and Kirk for asymptotically nonexpansive mappings. These are mappingsT:K→K satisfying, fori sufficiently large, ‖Tix−Tiy‖≦k
i‖x−y∼,x,y∈K, wherek
i→1 asi→∞. The precise assumption in (a) is somewhat weaker than uniform convexity, requiring only that Goebel’s characteristic of
convexity, ɛ0 (X), be less than one.
Research supported by National Science Foundation Grant GP 18045. 相似文献
3.
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
4.
E is a Banach lattice that is weakly sequentially complete and has a weak unitu. TLf
n=ϕ means that the infimum of |f
n−ϕ| andu converges strongly to zero.T is a positive contraction operator onE andA
n=(1/n)(I+T+...+T
n−1). Without an additional assumption onE, the “truncated limit” TLA
nf need not exist forf inE. This limit exists for eachf ifE satisfies the following additional assumption (C): For everyf inE
+ and for every numberα>0, there is a numberβ=β(f, α) such that ifg is inE
+, ‖g‖≦1, 0≦f′≦f and ‖f′‖>α then ‖f′+g‖≧‖g‖+β.
Research of this author is partially supported by NSERC Grant A3974.
Research of this author is partially supported by NSF Grant 8301619. 相似文献
5.
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
6.
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
7.
We say that A has fractional powers {A
t
}
t≥0 if there exists a nondegenerate C-regularized semigroup {W(t)}
t≥0 such that A=C
−1
W(1); then A
t
≡C
−1
W(t). We show that this generalizes the usual definition of fractional powers for nonnegative operators, and enables many operators
with spectrum containing the entire unit disc to have fractional powers. Our definition gives clear, simple proofs of the
basic properties of fractional powers. We show that, for nonnegative operators, the fractional powers with the property that,
if A is of type θ, then A
t
is of type t
θ, whenever t
θ<π, are unique. More generally, for injective G∈B(X) commuting with A, we show that an operator A of G-regularized type θ has a unique family of fractional powers with the property that A
t
is of G-regularized type t
θ whenever t
θ<π. This leads to a construction of fractional powers of operators with polynomially bounded resolvent outside of an appropriate
sector. We show that an operator is of regularized type if and only if it has exponentially bounded regularized imaginary
powers.
This work was done while the second author was visiting Ohio University, with funding from Universitat de València. He would
like to thank Ohio University and Professor deLaubenfels for their hospitality and support. 相似文献
8.
G. F. Webb 《Israel Journal of Mathematics》1972,12(3):237-248
It is shown that a strongly continuous semi-group of nonlinear nonexpansive operators can be constructed as lim
n→∞ ((I+t/nB)−1 (I+t/nB)−1)
n
whereA is a linearm-accretive operator,B is a nonlinearm-accretive operator, andB satisfies a boundedness condition relative toA. 相似文献
9.
Rajendra Bhatia 《印度理论与应用数学杂志》2010,41(1):99-111
Lipschitz continuity of the matrix absolute value |A| = (A*A)1/2 is studied. Let A and B be invertible, and let M
1 = max(‖A‖, ‖B‖), M
2 = max(‖A
−1‖, ‖B
−1‖). Then it is shown that
$
\left\| { \left| A \right| - \left| B \right| } \right\| \leqslant \left( {1 + log M_1 M_2 } \right) \left\| {A - B} \right\|
$
\left\| { \left| A \right| - \left| B \right| } \right\| \leqslant \left( {1 + log M_1 M_2 } \right) \left\| {A - B} \right\|
相似文献
10.
Abhijit Pal 《Proceedings Mathematical Sciences》2010,120(1):57-68
Let 1 → (K, K
1) → (G, N
G
(K
1)) → (Q, Q
1) → 1 be a short exact sequence of pairs of finitely generated groups with K
1 a proper non-trivial subgroup of K and K strongly hyperbolic relative to K
1. Assuming that, for all g ∈ G, there exists k
g
∈ K such that gK
1
g
−1 = k
g
K
1
k
g−1, we will prove that there exists a quasi-isometric section s: Q → G. Further, we will prove that if G is strongly hyperbolic relative to the normalizer subgroup N
G
(K
1) and weakly hyperbolic relative to K
1, then there exists a Cannon-Thurston map for the inclusion i: Γ
K
→ Γ
G
. 相似文献
11.
Some Simple Estimates for the Singular Values of Matrices 总被引:1,自引:0,他引:1
Chuan-long WANG Guo-jian ZHANGDepartment of Mathematics Normal College of Shanxi University Taiyuan ChinaDepartment of Applied Mathematics Taiyuan University of Technology Taiyuan China 《应用数学学报(英文版)》2002,18(1):117-122
Abstract We first provide a simple estimate for ||A~(-1)||_∞ and ||A~(-1)||_1 of a strictly diagonally dominant matrixA. On the Basis of the result, we obtain an estimate for the smallest singular value of A. Secondly, by scalingwith a positive diagonal matrix D, we obtain some simple estimates for the smallest singular value of an H-matrix, which is not necessarily positive definite. Finally, we give some examples to show the effectiveness ofthe new bounds. 相似文献
13.
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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