共查询到20条相似文献,搜索用时 46 毫秒
1.
Let τ be some triangulation of a planar polygonal domain Ω. Given a smooth functionu, we construct piecewise polynomial functionsv∈C
ρ(Ω) of degreen=3 ρ for ρ odd, andn=3ρ+1 for ρ even on a subtriangulation τ3 of τ. The latter is obtained by subdividing eachT∈ρ into three triangles, andv/T is a composite triangular finite element, generalizing the classicalC
1 cubic Hsieh-Clough-Tocher (HCT) triangular scheme. The functionv interpolates the derivatives ofu up to order ρ at the vertices of τ. Polynomial degrees obtained in this way are minimal in the family of interpolation schemes
based on finite elements of this type. 相似文献
2.
Aicke Hinrichs 《Archiv der Mathematik》1997,68(4):265-273
Let A
n
=(a
1,...,a
n) be a system of characters of a compact abelian group A
n
with normalized Haar measure μ and let T be a bounded linear operator from a Banach space X into a Banach space Y. The type norm τ(T|
A
n
) of T with respect to A
n
is the least constant c such that
for all x
1,..., x
n ∈ X. We investigate under which conditions on two systems A
n
and ℬ
n
of characters of compact abelian groups an inequality τ(T|ℬ
n) ≦ τ(T|A
n
) holds for all linear bounded operators T between Banach spaces. It turns out that this can be tested on a certain operator depending only on the system ℬ
n. Moreover, it is equivalent to strong algebraic relations between A
n
and ℬ
n as well as to relations between its distributions. In particular, for systems of trigonometric functions this inequality
for all linear bounded operators even implies equality for all linear bounded operators.
The author is supported by DFG grant PI 322/1-1. The content of this paper is part of the authors PhD-thesis written under
the supervision of A. Pietsch. 相似文献
3.
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
4.
E.K. Ifantis C.G. Kokologiannaki E. Petropoulou 《Central European Journal of Mathematics》2007,5(2):335-344
Let T be a self-adjoint tridiagonal operator in a Hilbert space H with the orthonormal basis {e
n
}
n=1
∞
, σ(T) be the spectrum of T and Λ(T) be the set of all the limit points of eigenvalues of the truncated operator T
N
. We give sufficient conditions such that the spectrum of T is discrete and σ(T) = Λ(T) and we connect this problem with an old problem in analysis.
相似文献
6.
Composition Operators on the Bloch Space of Several Complex Variables 总被引:19,自引:0,他引:19
Abstract
In this paper, we study the boundedness and compactness of composition operator C
φ on the Bloch space β(Ω), Ω being a bounded homogeneous domain. For Ω = B
n, we give the necessary and sufficient conditions for a composition operator C
φ to be compact on β(B
n) or β
0(B
n).
Supported by the National Natural Science Foundation and the National Education Committee Doctoral
Foundation 相似文献
7.
Let L(H) denote the algebra of all bounded linear operators on a separable infinite dimensional complex Hilbert space H into itself. Given A ∈ L(H), we define the elementary operator Δ
A
: L(H) → L(H) by Δ
A
(X) = AXA − X. In this paper we study the class of operators A ∈ L(H) which have the following property: ATA = T implies AT*A = T* for all trace class operators T ∈ C
1(H). Such operators are termed generalized quasi-adjoints. The main result is the equivalence between this character and the
fact that the ultraweak closure of the range of Δ
A
is closed under taking adjoints. We give a characterization and some basic results concerning generalized quasi-adjoints
operators. 相似文献
8.
Ingo Steinwart 《Journal of Approximation Theory》2000,103(2):17
We investigate how the entropy numbers (en(T)) of an arbitrary Hölder-continuous operator T: E→C(K) are influenced by the entropy numbers (n(K)) of the underlying compact metric space K and the geometry of E. We derive diverse universal inequalities relating finitely many n(K)'s with finitely many en(T)'s which yield statements about the asymptotically optimal behaviour of the sequence (en(T)) in terms of the sequence (n(K)). As an application we present new methods for estimating the entropy numbers of a precompact and convex subset in a Banach space E, provided that the entropy numbers of its extremal points are known. 相似文献
9.
LetK be a compact Hausdorff space, and letT be an irreducible Markov operator onC(K). We show that ifgεC(K) satisfies sup
N
‖Σ
j
=0N
T
j
g‖<∞, then (and only then) there existsfεC(K) with (I − T)f=g. Generalizing the result to irreducible Markov operator representations of certain semi-groups, we obtain that bounded cocycles
are (continuous) coboundaries. For minimal semi-group actions inC(K), no restriction on the semi-group is needed. 相似文献
10.
Kunyu Guo 《Arkiv f?r Matematik》2000,38(1):97-110
For an essentially normal operatorT, it is shown that there exists a unilateral shift of multiplicitym inC
*
(T) if and only if γ(T)≠0 and γ(T)/m. As application, we prove that the essential commutant of a unilateral shift and that of a bilateral shift are not isomorphic
asC
*
-algebras. Finally, we construct a naturalC
*
-algebra ε + ε* on the Bergman spaceL
a
2
(B
n
), and show that its essential commutant is generated by Toeplitz operators with symmetric continuous symbols and all compact
operators.
Supported by NSFC and Laboratory of Mathematics for Nonlinear Science at Fudan University. 相似文献
11.
Let X be a Banach space, K be a scattered compact and T: B
C(K) → X be a Fréchet smooth operator whose derivative is uniformly continuous. We introduce the smooth biconjugate T**: B
C(K)** → X** and prove that if T is noncompact, then the derivative of T** at some point is a noncompact linear operator. Using this we conclude, among other things, that either
is compact or that ℓ1 is a complemented subspace of X*. We also give some relevant examples of smooth functions and operators, in particular, a C
1,u
-smooth noncompact operator from B
c
O which does not fix any (affine) basic sequence.
P. Hájek was supported by grants A100190502, Institutional Research Plan AV0Z10190503. 相似文献
12.
A bounded linear operator between Banach spaces is calledcompletely continuous if it carries weakly convergent sequences into norm convergent sequences. Isolated is a universal operator for the class
of non-completely-continuous operators fromL
1 into an arbitrary Banach space, namely, the operator fromL
1 into ⊆∞ defined byT
0(f) = (∫r
n
f
d
μ)
n>-0, wherer
n
is thenth Rademacher function. It is also shown that there does not exist a universal operator for the class of non-completely-continuous
operators between two arbitrary Banach spaces. The proof uses the factorization theorem for weakly compact operators and a
Tsirelson-like space.
Supported in part by NSF grant DMS-9306460. Participant, NSF Workshop in Linear Analysis & Probability, Texas A&M University
(supported in part by NSF grant DMS-9311902).
Supported in part by NSF grant DMS-9003550. 相似文献
13.
Let (S)⊄L
2(S′(∔),μ)⊄(S)* be the Gel'fand triple over the white noise space (S′(∔),μ). Let (e
n
,n>-0) be the ONB ofL
2(∔) consisting of the eigenfunctions of the s.a. operator
. In this paper the Euler operator Δ
E
is defined as the sum
, where ∂
i
stands for the differential operatorD
e
i. It is shown that Δ
E
is the infinitesimal generator of the semigroup (T
t
), where (T
t
ϕ)(x)=ϕ(e
t
x) for ϕ∈(S). Similarly to the finite dimensional case, the λ-order homogeneous test functionals are characterized by the Euler equation:
Δ
Eϕ
=λϕ. Via this characterization the λ-order homogeneous Hida distributions are defined and their properties are worked out.
Supported by the National Natural Science Foundation of China. 相似文献
14.
Let (Ω, Σ) be a measurable space, X a Banach space whose characteristic of noncompact convexity is less than 1, C a bounded closed convex subset of X, KC(C) the family of all compact convex subsets of C. We prove that a set-valued nonexpansive mapping T: C → KC(C) has a fixed point. Furthermore, if X is separable then we also prove that a set-valued nonexpansive operator T: Ω × C → KC(C) has a random fixed point. 相似文献
15.
Let K be an absolutely convex infinite-dimensional compact in a Banach space χ. The set of all bounded linear operators T on χ satisfying TK ⊃ K is denoted by G(K). Our starting point is the study of the closure WG(K) of G(K) in the weak operator topology. We prove that WG(K) contains the algebra of all operators leaving [`(lin(K))]\overline{{\rm lin}(K)} invariant. More precise results are obtained in terms of the Kolmogorov n-widths of the compact K. The obtained results are used in the study of operator ranges and operator equations. 相似文献
16.
LetS be a topological semigroup andAP(S) the space of continous complex almost periodic functions onS. We obtain characterizations of compact and weakly compact operators from a Banach spaceX into AP(S). For this we use the almost periodic compactification ofS obtained through uniform spaces. For a bounded linear operatorT fromX into AP(S), letT
5, be the translate ofT bys inS defined byT
5(x)=(Tx)
5
. We define topologies on the space of bounded linear operators fromX into AP(S) and obtain the necessary and sufficient conditions for an operatorT to be compact or weakly compact in terms of the uniform continuity of the maps→T
5. IfS is a Hausdorff topological semigroup, we also obtain characterizations of compact and weakly compact multipliers on AP(S) in terms of the uniform continuity of the map S→μs, where μs denotes the unique vector measure corresponding to the operatorT
5. 相似文献
17.
F. Luca I. E. Shparlinski 《Abhandlungen aus dem Mathematischen Seminar der Universit?t Hamburg》2006,76(1):143-156
Let (un)n≥0 be a non-degenerate linear recurrence sequence of integers. We show that the set of positive integersn such that either ω)(n) orΩ(n) dividesu
n
is of asymptotic density zero, where ω(n) and Ω(n) are the numbers of prime and prime power divisors ofn, respectively. The same also holds for the set of positive integersn such that τ(n)u
n
, where τ(n) is the number of the positive integer divisors of n, provided thatu
n
satisfies some mild technical conditions. 相似文献
18.
We consider the elliptic operator Lu(x):= xu″(x)+β(x)u′(x) + γ (x)u(x) with Wentzell-type boundary condition, in spaces of continuous function on [0,+∞[. We prove that such operators generate
positive C
0-semigroup which can be approximated by means of iterated of modified Szász-Mirakjan operators here introduced. 相似文献
19.
Alaa E. Hamza 《Journal of Difference Equations and Applications》2013,19(3):233-253
We suppose that M is a closed subspace of l ∞(J, X), the space of all bounded sequences {x(n)} n?J ? X, where J ? {Z+,Z} and X is a complex Banach space. We define the M-spectrum σM (u) of a sequence u ? l ∞(J,X). Certain conditions will be supposed on both M and σM (u) to insure the existence of u ? M. We prove that if u is ergodic, such that σM (u,) is at most countable and, for every λ ? σM (u), the sequence e?iλnu(n) is ergodic, then u ? M. We apply this result to the operator difference equationu(n + 1) = Au(n) + ψ(n), n ? J,and to the infinite order difference equation Σ r k=1 ak (u(n + k) ? u(n)) + Σ s ? Z?(n ? s)u(s) = h(n), n?J, where ψ?l ∞(Z,X) such that ψ| J ? M, A is the generator of a C 0-semigroup of linear bounded operators {T(t)} t>0 on X, h ? M, ? ? l 1(Z) and ak ?C. Certain conditions will be imposed to guarantee the existence of solutions in the class M. 相似文献
20.
In this note we introduce and study the property (gw), which extends property (w) introduced by Rakoc̆evic in [23]. We investigate the property (gw) in connection with Weyl type theorems. We show that if T is a bounded linear operator T acting on a Banach space X, then property (gw) holds for T if and only if property (w) holds for T and Π
a
(T) = E(T), where Π
a
(T) is the set of left poles of T and E(T) is the set of isolated eigenvalues of T. We also study the property (gw) for operators satisfying the single valued extension property (SVEP). Classes of operators are considered as illustrating
examples.
The second author was supported by Protars D11/16 and PGR- UMP. 相似文献