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 ) → L p ( ν ) , each n ∈ ℕ and functions f 1 , . . . , f n ∈ L q ( μ ) , ( ʃ ( ∑ k = 1 n | T f k | r ) p / r d ν ) 1 / p ≤ c ∥ T ∥ ( ʃ ( ∑ 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 ≤ 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 ≥ 0 and ∃ M < ∞ such that ∥ H n ( s ) ∥ ≡ ∥ ( ∑ k = 0 n ( s k A k ) / k ! ) e - s A ∥ ≤ 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|)...

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).

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.