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Displaying similar documents to “A zero-two theorem for a certain class of positive contractions in finite dimensional L P -spaces ( 1 p < + )

Semivariation in L p -spaces

Brian Jefferies, Susumu Okada (2005)

Commentationes Mathematicae Universitatis Carolinae

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Suppose that X and Y are Banach spaces and that the Banach space X ^ τ Y is their complete tensor product with respect to some tensor product topology τ . A uniformly bounded X -valued function need not be integrable in X ^ τ Y with respect to a Y -valued measure, unless, say, X and Y are Hilbert spaces and τ is the Hilbert space tensor product topology, in which case Grothendieck’s theorem may be applied. In this paper, we take an index 1 p < and suppose that X and Y are L p -spaces with τ p the associated...

Ergodic properties of contraction semigroups in L p , 1 < p <

Ryotaro Sato (1994)

Commentationes Mathematicae Universitatis Carolinae

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Let { T ( t ) : t > 0 } be a strongly continuous semigroup of linear contractions in L p , 1 < p < , of a σ -finite measure space. In this paper we prove that if there corresponds to each t > 0 a positive linear contraction P ( t ) in L p such that | T ( t ) f | P ( t ) | f | for all f L p , then there exists a strongly continuous semigroup { S ( t ) : t > 0 } of positive linear contractions in L p such that | T ( t ) f | S ( t ) | f | for all t > 0 and f L p . Using this and Akcoglu’s dominated ergodic theorem for positive linear contractions in L p , we also prove multiparameter pointwise ergodic and local ergodic...

Cauchy problem for the complex Ginzburg-Landau type Equation with L p -initial data

Daisuke Shimotsuma, Tomomi Yokota, Kentarou Yoshii (2014)

Mathematica Bohemica

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This paper gives the local existence of mild solutions to the Cauchy problem for the complex Ginzburg-Landau type equation u t - ( λ + i α ) Δ u + ( κ + i β ) | u | q - 1 u - γ u = 0 in N × ( 0 , ) with L p -initial data u 0 in the subcritical case ( 1 q < 1 + 2 p / N ), where u is a complex-valued unknown function, α , β , γ , κ , λ > 0 , p > 1 , i = - 1 and N . The proof is based on the L p - L q estimates of the linear semigroup { exp ( t ( λ + i α ) Δ ) } and usual fixed-point argument.