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It is proved that if a Kothe sequence space $X$ is monotone complete and has the weakly convergent sequence coefficient WCS $(X) > 1$ , then $X$ is order continuous. It is shown that a weakly sequentially complete Kothe sequence space $X$ is compactly locally uniformly rotund if and only if the norm in $X$ is equi-absolutely continuous. The dual of the product space ${(⨁_{i = 1}^{\infty} X_{i})}_{Φ}$ of a sequence of Banach spaces ${(X_{i})}_{i = 1}^{\infty}$ , which is built by using an Orlicz function $Φ$ satisfying the $Δ_{2}$ -condition, is computed isometrically (i.e. the exact...

On the dependence of the orthogonal projector on deformations of the scalar product

Zbigniew Pasternak-Winiarski (1998)

Studia Mathematica

We consider scalar products on a given Hilbert space parametrized by bounded positive and invertible operators defined on this space, and orthogonal projectors onto a fixed closed subspace of the initial Hilbert space corresponding to these scalar products. We show that the projector is an analytic function of the scalar product, we give the explicit formula for its Taylor expansion, and we prove some algebraic formulas for projectors.

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On a class of Banach spaces of analytic functions.

On a weighted Toeplitz operator and its commutant.

On convexity of composition and multiplication operators on weighted Hardy spaces.

On cyclicity in weighted Dirichlet spaces.

On Hadamard-Dirichlet algebras.

On multipliers of temperate distributions

On some geometric properties of certain Köthe sequence spaces

On the dependence of the orthogonal projector on deformations of the scalar product

On the Forelli-Rudin construction and weighted Bergman projections

Optimal Sampling of Holomorphic Fuctions. II.

Orthogonal Trigonometric Schauder Bases of Optimal Degree for C(K).

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