EuDML | Browse

Items

All a b c d e f g h i j k l m n o p q r s t u v w x y z Other

Displaying 1161 – 1180 of 1952

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.

On the derived tensor product functors for (DF)- and Fréchet spaces

Oğuz Varol (2007)

Studia Mathematica

For a (DF)-space E and a tensor norm α we investigate the derivatives $T o r_{α}^{l} (E, \cdot)$ of the tensor product functor $E \otimes ̃_{α} \cdot : \to$ from the category of Fréchet spaces to the category of linear spaces. Necessary and sufficient conditions for the vanishing of $T o r ¹_{α} (E, F)$ , which is strongly related to the exactness of tensored sequences, are presented and characterizations in the nuclear and (co-)echelon cases are given.

On the diagonal of matrix transformations

Juan Carlos Díaz (1998)

Revista de la Real Academia de Ciencias Exactas Físicas y Naturales

On the diameter of the Banach-Mazur set

Gilles Godefroy (2010)

Czechoslovak Mathematical Journal

On every subspace of $l_{\infty} (ℕ)$ which contains an uncountable $ω$ -independent set, we construct equivalent norms whose Banach-Mazur distance is as large as required. Under Martin’s Maximum Axiom (MM), it follows that the Banach-Mazur diameter of the set of equivalent norms on every infinite-dimensional subspace of $l_{\infty} (ℕ)$ is infinite. This provides a partial answer to a question asked by Johnson and Odell.

On the diametral dimension of weighted spaces of analytic germs

Michael Langenbruch (2016)

Studia Mathematica

We prove precise estimates for the diametral dimension of certain weighted spaces of germs of holomorphic functions defined on strips near ℝ. This implies a full isomorphic classification for these spaces including the Gelfand-Shilov spaces $S ¹_{α}$ and $S ₁^{α}$ for α > 0. Moreover we show that the classical spaces of Fourier hyperfunctions and of modified Fourier hyperfunctions are not isomorphic.

On the differences of the consecutive powers of Banach algebra elements

Helmuth Rönnefarth (1997)

Banach Center Publications

Let A denote a complex unital Banach algebra. We characterize properties such as boundedness, relative compactness, and convergence of the sequence ${x^{n} (x - 1)}_{n \in ℕ}$ for an arbitrary x ∈ A, using σ(x) and resolvent conditions. Under these circumstances, we investigate elements in the peripheral spectrum, and give further conclusions, also involving the behaviour of ${x^{n}}_{n \in ℕ}$ and ${1 / n \sum_{k = 0}^{n - 1} x^{k}}_{n \in ℕ}$ .

On the differentiability of Lipschitz mappings in Fréchet spaces

P. Mankiewicz (1973)

Studia Mathematica