Four characterizations of scalar-type operators with spectrum in a half-line

Peter Vieten

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Displaying similar documents to “Four characterizations of scalar-type operators with spectrum in a half-line”

The Grothendieck-Pietsch domination principle for nonlinear summing integral operators

Karl Lermer (1998)

Studia Mathematica

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We transform the concept of p-summing operators, 1≤ p < ∞, to the more general setting of nonlinear Banach space operators. For 1-summing operators on B(Σ,X)-spaces having weak integral representations we generalize the Grothendieck-Pietsch domination principle. This is applied for the characterization of 1-summing Hammerstein operators on C(S,X)-spaces. For p-summing Hammerstein operators we derive the existence of control measures and p-summing extensions to B(Σ,X)-spaces. ...

Best constants and asymptotics of Marcinkiewicz-Zygmund inequalities

Andreas Defant, Marius Junge (1997)

Studia Mathematica

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We determine the set of all triples 1 ≤ p,q,r ≤ ∞ for which the so-called Marcinkiewicz-Zygmund inequality is satisfied: There exists a constant c≥ 0 such that for each bounded linear operator $T : L_{q} (μ) \to L_{p} (ν)$ , each n ∈ ℕ and functions $f_{1}, . . ., f_{n} \in L_{q} (μ)$ , $(ʃ (\sum_{k = 1}^{n} | T f_{k} |^{r})^{p / r} {d ν)}^{1 / p} \leq c ∥ T ∥ (ʃ (\sum_{k = 1}^{n} | f_{k} |^{r} {)^{q / r} d μ)}^{1 / q}$ . This type of inequality includes as special cases well-known inequalities of Paley, Marcinkiewicz, Zygmund, Grothendieck, and Kwapień. If such a Marcinkiewicz-Zygmund inequality holds for a given triple (p,q,r), then we calculate the best constant c ≥ 0 (with the...

Unbounded well-bounded operators, strongly continuous semigroups and the Laplace transform

Ralph deLaubenfels (1992)

Studia Mathematica

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Suppose A is a (possibly unbounded) linear operator on a Banach space. We show that the following are equivalent. (1) A is well-bounded on [0,∞). (2) -A generates a strongly continuous semigroup ${e^{- s A}}_{s \leq 0}$ such that ${(1 / s^{2}) e^{- s A}}_{s > 0}$ is the Laplace transform of a Lipschitz continuous family of operators that vanishes at 0. (3) -A generates a strongly continuous differentiable semigroup ${e^{- s A}}_{s \geq 0}$ and ∃ M < ∞ such that $∥ H_{n} (s) ∥ \equiv ∥ (\sum_{k = 0}^{n} (s^{k} A^{k}) / k!) e^{- s A} ∥ \leq M$ , ∀s > 0, n ∈ ℕ ∪ 0. (4) -A generates a strongly continuous holomorphic semigroup ${e^{- z A}}_{R e (z) > 0}$ that is O(|z|)...

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E. Sawyer (1990)

Studia Mathematica

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Dominated operators on C[0, 1] and the (CRP).

G. Emmanuele (1990)

Collectanea Mathematica

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We show that a B-space E has the (CRP) if and only if any dominated operator T from C[0, 1] into E is compact. Hence we apply this result to prove that c0 embeds isomorphically into the B-space of all compact operators from C[0, 1] into an arbitrary B-space E without the (CRP).

Spectral analysis of perturbed multiplication operators occurring in polymerization chemistry

Niels Joergen Kokholm (1989)

Journées équations aux dérivées partielles

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Compact AC-operators

Ian Doust, Byron Walden (1996)

Studia Mathematica

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We prove that compact AC-operators have a representation as a combination of disjoint projections which mirrors that for compact normal operators. We also show that unlike arbitrary AC-operators, compact AC-operators admit a unique splitting into real and imaginary parts, and that these parts must necessarily be compact.

Almost sure approximation of unbounded operators in $L_{2} (X, A, μ)$

Ryszard Jajte, Adam Paszkiewicz (1998)

Studia Mathematica

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The possibilities of almost sure approximation of unbounded operators in $L_{2} (X, A, μ)$ by multiples of projections or unitary operators are examined.

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Thomas J. Ransford (1990)

Séminaire de probabilités de Strasbourg

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On the asymptotic behavior of solutions of linear parabolic equations in $L^{1}$ space

Dong Gun Park, Hiroki Tanabe (1987)

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