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Adaptive wavelet methods for saddle point problems

Stephan Dahlke, Reinhard Hochmuth, Karsten Urban (2010)

ESAIM: Mathematical Modelling and Numerical Analysis

Recently, adaptive wavelet strategies for symmetric, positive definite operators have been introduced that were proven to converge. This paper is devoted to the generalization to saddle point problems which are also symmetric, but indefinite. Firstly, we investigate a posteriori error estimates and generalize the known adaptive wavelet strategy to saddle point problems. The convergence of this strategy for elliptic operators essentially relies on the positive definite character of the operator....

Additive combinations of special operators

Pei Wu (1994)

Banach Center Publications

This is a survey paper on additive combinations of certain special-type operators on a Hilbert space. We consider (finite) linear combinations, sums, convex combinations and/or averages of operators from the classes of diagonal operators, unitary operators, isometries, projections, symmetries, idempotents, square-zero operators, nilpotent operators, quasinilpotent operators, involutions, commutators, self-commutators, norm-attaining operators, numerical-radius-attaining operators, irreducible operators...

Addresses

(1979)

Abstracta. 7th Winter School on Abstract Analysis

Adjoint bi-continuous semigroups and semigroups on the space of measures

Bálint Farkas (2011)

Czechoslovak Mathematical Journal

For a given bi-continuous semigroup ( T ( t ) ) t 0 on a Banach space X we define its adjoint on an appropriate closed subspace X of the norm dual X ' . Under some abstract conditions this adjoint semigroup is again bi-continuous with respect to the weak topology σ ( X , X ) . We give the following application: For Ω a Polish space we consider operator semigroups on the space C b ( Ω ) of bounded, continuous functions (endowed with the compact-open topology) and on the space M ( Ω ) of bounded Baire measures (endowed with the weak * -topology)....

Adjoint characterisations of unbounded weakly compact, weakly completely continuous and unconditionally converging operators

T. Alvarez, R. Cross, A. Gouveia (1995)

Studia Mathematica

Characterisations are obtained for the following classes of unbounded linear operators between normed spaces: weakly compact, weakly completely continuous, and unconditionally converging operators. Examples of closed unbounded operators belonging to these classes are exhibited. A sufficient condition is obtained for the weak compactness of T' to imply that of T.

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