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Displaying 301 – 320 of 658

On continuous composition operators

Wilhelmina Smajdor (2010)

Annales Polonici Mathematici

Let I ⊂ ℝ be an interval, Y be a normed linear space and Z be a Banach space. We investigate the Banach space Lip₂(I,Z) of all functions ψ: I → Z such that $M_{ψ} : = s u p | | [r, s, t; ψ] | | : r < s < t, r, s, t \in I < \infty$ , where [r,s,t;ψ]:= ((s-r)ψ(t)+(t-s)ψ(r)-(t-r)ψ(s))/((t-r)(t-s)(s-r)). We show that ψ ∈ Lip₂(I,Z) if and only if ψ is differentiable and its derivative ψ’ is Lipschitzian. Suppose the composition operator N generated by h: I × Y → Z, (Nφ)(t):= h(t,φ(t)), maps the set (I,Y) of all affine functions φ: I → Y into Lip₂(I,Z). We prove that if N is...

On convergence of iterates of the Frobenius-Perron operator for expanding mappings

Marian Jabłoński (1988)

Annales Polonici Mathematici

On dyadic spaces and almost Milyutin spaces

José Blasco, C. Ivorra (1994)

Colloquium Mathematicae

On Erb's uncertainty principle

Hubert Klaja (2016)

Studia Mathematica

We improve a result of Erb, concerning an uncertainty principle for orthogonal polynomials. The proof uses numerical range and a decomposition of some multiplication operators as a difference of orthogonal projections.

On essential norm of the Neumann operator

Dagmar Medková (1992)

Mathematica Bohemica

One of the classical methods of solving the Dirichlet problem and the Neumann problem in $𝐑^{m}$ is the method of integral equations. If we wish to use the Fredholm-Radon theory to solve the problem, it is useful to estimate the essential norm of the Neumann operator with respect to a norm on the space of continuous functions on the boundary of the domain investigated, where this norm is equivalent to the maximum norm. It is shown in the paper that under a deformation of the domain investigated by a diffeomorphism,...

On extreme operators

G. Mägerl (1982)

Colloquium Mathematicae

On integral operators with operator-valued kernels.

Shahmurov, Rishad (2010)

Journal of Inequalities and Applications [electronic only]

On Integral Representations and a priori Lipschitz Estimates for the Canonical Solution of the ...-Equation.

Ingo Lieb, R.Michael Range (1983)

Mathematische Annalen

On invariant functions and ergodic measures of Markov operators on C(X)

Ryszard Rębowski (1987)

Colloquium Mathematicae

On isometric domains of positive operators on $L^{p}$ -spaces

Ryszard Grząślewicz (1987)

Colloquium Mathematicae

On isometric domains of positive operators on orlicz spaces

Grząślewicz, Ryszard (1982)

Proceedings of the 10th Winter School on Abstract Analysis

On isomorphisms of some Köthe function F-spaces

Violetta Kholomenyuk, Volodymyr Mykhaylyuk, Mikhail Popov (2011)

Open Mathematics

We prove that if Köthe F-spaces X and Y on finite atomless measure spaces (ΩX; ΣX, µX) and (ΩY; ΣY; µY), respectively, with absolute continuous norms are isomorphic and have the property $lim_{μ (A) \to 0} ∥μ {(A)}^{- 1} 1_{A}∥ = 0$ (for µ = µX and µ = µY, respectively) then the measure spaces (ΩX; ΣX; µX) and (ΩY; ΣY; µY) are isomorphic, up to some positive multiples. This theorem extends a result of A. Plichko and M. Popov concerning isomorphic classification of L p(µ)-spaces for 0 < p < 1. We also provide a new class of F-spaces...

On $L_{p} - L_{q}$ boundedness for convolutions with kernels having singularities on a sphere

Alexey N. Karapetyants (2001)

Studia Mathematica

For the convolution operators $A_{a}^{α}$ with symbols ${a (| ξ |) | ξ |}^{- α} e x p i | ξ |$ , 0 ≤ Re α < n, $a (| ξ |) \in L_{\infty}$ , we construct integral representations and give the exact description of the set of pairs (1/p,1/q) for which the operators are bounded from $L_{p}$ to $L_{q}$ .

On Lebesgue pseudonorms on $C_{0} (T)$

Ivan Dobrakov (1982)

Mathematica Slovaca

On Musielak-Orlicz spaces isometric to L2 or L∞.

Anna Kaminska (1997)

Collectanea Mathematica

It is proved that a Musielak-Orlicz space LΦ of real valued functions which is isometric to a Hilbert space coincides with L2 up to a weight, that is Φ(u,t) = c(t) u2. Moreover it is shown that any surjective isometry between LΦ and L∞ is a weighted composition operator and a criterion for LΦ to be isometric to L∞ is presented.

On nonintegrality of functions of some integral and partially integral operators.

Korotkov, V.B. (2000)

Sibirskij Matematicheskij Zhurnal

On norm attaining operators acting from $L^{1} (μ)$ to C (S)

Iwanik, A. (1982)

Proceedings of the 10th Winter School on Abstract Analysis

On Operators in Bochner Spaces

Nina A. Yerzakova (1997)

Matematički Vesnik

On operators on $L_{0}$

N. J. Kalton (1984)

Colloquium Mathematicae

On order structure and operators in L ∞(μ)

Irina Krasikova, Miguel Martín, Javier Merí, Vladimir Mykhaylyuk, Mikhail Popov (2009)

Open Mathematics

It is known that there is a continuous linear functional on L ∞ which is not narrow. On the other hand, every order-to-norm continuous AM-compact operator from L ∞(μ) to a Banach space is narrow. We study order-to-norm continuous operators acting from L ∞(μ) with a finite atomless measure μ to a Banach space. One of our main results asserts that every order-to-norm continuous operator from L ∞(μ) to c 0(Γ) is narrow while not every such an operator is AM-compact.

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