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Displaying 341 – 360 of 1952

On decompositions of Banach spaces into a sum of operator ranges

V. Fonf, V. Shevchik (1999)

Studia Mathematica

It is proved that a separable Banach space X admits a representation $X = X_{1} + X_{2}$ as a sum (not necessarily direct) of two infinite-codimensional closed subspaces $X_{1}$ and $X_{2}$ if and only if it admits a representation $X = A_{1} (Y_{1}) + A_{2} (Y_{2})$ as a sum (not necessarily direct) of two infinite-codimensional operator ranges. Suppose that a separable Banach space X admits a representation as above. Then it admits a representation $X = T_{1} (Z_{1}) + T_{2} (Z_{2})$ such that neither of the operator ranges $T_{1} (Z_{1})$ , $T_{2} (Z_{2})$ contains an infinite-dimensional closed subspace if and only...

On deductive varieties of locally convex spaces

Sergej M. Berger (1988)

Commentationes Mathematicae Universitatis Carolinae

On defining the generalized functions $δ^{α} (z)$ and $δ^{n} (x)$ .

Koh, E.K., Li, C.K. (1993)

International Journal of Mathematics and Mathematical Sciences

On defining the product $r^{- k} \cdot \nabla^{l} δ$ .

Li, C.K., Zou, V. (2004)

International Journal of Mathematics and Mathematical Sciences

On Denjoy type extensions of the Pettis integral

Kirill Naralenkov (2010)

Czechoslovak Mathematical Journal

In this paper two Denjoy type extensions of the Pettis integral are defined and studied. These integrals are shown to extend the Pettis integral in a natural way analogous to that in which the Denjoy integrals extend the Lebesgue integral for real-valued functions. The connection between some Denjoy type extensions of the Pettis integral is examined.

On Denjoy-Dunford and Denjoy-Pettis integrals

José Gámez, José Mendoza (1998)

Studia Mathematica

The two main results of this paper are the following: (a) If X is a Banach space and f : [a,b] → X is a function such that x*f is Denjoy integrable for all x* ∈ X*, then f is Denjoy-Dunford integrable, and (b) There exists a Dunford integrable function $f : [a, b] \to c_{0}$ which is not Pettis integrable on any subinterval in [a,b], while $ʃ_{J} f$ belongs to $c_{0}$ for every subinterval J in [a,b]. These results provide answers to two open problems left by R. A. Gordon in [4]. Some other questions in connection with Denjoy-Dundord...

On dense ideals in spaces of analytic functions

Mihai Putinar (1994)

Annales de l'institut Fourier

One proves the density of an ideal of analytic functions into the closure of analytic functions in a $L^{p} (μ)$ -space, under some geometric conditions on the support of the measure $μ$ and the zero variety of the ideal.

On dense ideals of C*-algebras and generalizations of the Gelfand-Naimark Theorem

Jorma Arhippainen, Jukka Kauppi (2013)

Studia Mathematica

We develop the theory of Segal algebras of commutative C*-algebras, with an emphasis on the functional representation. Our main results extend the Gelfand-Naimark Theorem. As an application, we describe faithful principal ideals of C*-algebras. A key ingredient in our approach is the use of Nachbin algebras to generalize the Gelfand representation theory.

On derivations and crossed homomorphisms

Viktor Losert (2010)

Banach Center Publications

We discuss some results about derivations and crossed homomorphisms arising in the context of locally compact groups and their group algebras, in particular, L¹(G), the von Neumann algebra VN(G) and actions of G on related algebras. We answer a question of Dales, Ghahramani, Grønbæk, showing that L¹(G) is always permanently weakly amenable. Then we show that for some classes of groups (e.g. IN-groups) the homology of L¹(G) with coefficients in VN(G) is trivial. But this is no longer true, in general,...

On derivations on certain function spaces and their relation to the differential operator. (Über Derivationen auf gewissen Funktionenräumen und deren Beziehung zum Differentiationsoperator.)

Powa̧zka, Zbigniew, Rose, Michael (1994)

Mathematica Pannonica

On diffeomorphisms deleting weak compacta in Banach spaces

Daniel Azagra, Alejandro Montesinos (2004)

Studia Mathematica

We prove that if X is an infinite-dimensional Banach space with $C^{p}$ smooth partitions of unity then X and X∖ K are $C^{p}$ diffeomorphic for every weakly compact set K ⊂ X.

On differences of Riesz homomorphisms.

Kutateladze, S.S. (2005)

Sibirskij Matematicheskij Zhurnal

On differentiability of strongly α(·)-paraconvex functions in non-separable Asplund spaces

S. Rolewicz (2005)

Studia Mathematica

In Rolewicz (2002) it was proved that every strongly α(·)-paraconvex function defined on an open convex set in a separable Asplund space is Fréchet differentiable on a residual set. In this paper it is shown that the assumption of separability is not essential.

On differentiability of the extremals of variational integrals

Giaquinta, Mariano (1982)

Nonlinear Analysis, Function Spaces and Applications

On differentiability properties of Lipschitz functions on a Banach space with a Lipschitz uniformly Gâteaux differentiable bump function

Luděk Zajíček (1997)

Commentationes Mathematicae Universitatis Carolinae

We improve a theorem of P.G. Georgiev and N.P. Zlateva on Gâteaux differentiability of Lipschitz functions in a Banach space which admits a Lipschitz uniformly Gâteaux differentiable bump function. In particular, our result implies the following theorem: If $d$ is a distance function determined by a closed subset $A$ of a Banach space $X$ with a uniformly Gâteaux differentiable norm, then the set of points of $X ∖ A$ at which $d$ is not Gâteaux differentiable is not only a first category set, but it is even $σ$ -porous...

Currently displaying 341 – 360 of 1952

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Displaying 341 – 360 of 1952

On decompositions of Banach spaces into a sum of operator ranges

On deductive varieties of locally convex spaces

On defining the generalized functions $δ^{α} (z)$ and $δ^{n} (x)$ .

On defining the product $r^{- k} \cdot \nabla^{l} δ$ .

On Denjoy type extensions of the Pettis integral

On Denjoy-Dunford and Denjoy-Pettis integrals

On dense ideals in spaces of analytic functions

On dense ideals of C*-algebras and generalizations of the Gelfand-Naimark Theorem

On derivations and crossed homomorphisms

On derivations on certain function spaces and their relation to the differential operator. (Über Derivationen auf gewissen Funktionenräumen und deren Beziehung zum Differentiationsoperator.)

On diffeomorphisms deleting weak compacta in Banach spaces

On differences of Riesz homomorphisms.

On differentiability of strongly α(·)-paraconvex functions in non-separable Asplund spaces

On differentiability of the extremals of variational integrals

On differentiability properties of Lipschitz functions on a Banach space with a Lipschitz uniformly Gâteaux differentiable bump function

On differential subspaces of Cartesian space

On differentiation of metric projections in finite dimensional Banach spaces

On dilation operators in Besov spaces.

On discontinuity of the spectral radius in Banach algebras

On Discontinuous Homomorphisms of L1(G).

Currently displaying 341 – 360 of 1952