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Bruno de Mendonça Braga (0)

Annales de l’institut Fourier

Upper and lower estimates in Banach sequence spaces

Raquel Gonzalo (1995)

Commentationes Mathematicae Universitatis Carolinae

Here we study the existence of lower and upper p -estimates of sequences in some Banach sequence spaces. We also compute the sharp p estimates in their basis. Finally, we give some applications to weak sequential continuity of polynomials.

w * -basic sequences and reflexivity of Banach spaces

Kamil John (2005)

Czechoslovak Mathematical Journal

We observe that a separable Banach space X is reflexive iff each of its quotients with Schauder basis is reflexive. Similarly if ( X , Y ) is not reflexive for reflexive X and Y then ( X 1 , Y ) is is not reflexive for some X 1 X , X 1 having a basis.

Weak Convergence and Weak Convergence

Keiko Narita, Yasunari Shidama, Noboru Endou (2015)

Formalized Mathematics

In this article, we deal with weak convergence on sequences in real normed spaces, and weak* convergence on sequences in dual spaces of real normed spaces. In the first section, we proved some topological properties of dual spaces of real normed spaces. We used these theorems for proofs of Section 3. In Section 2, we defined weak convergence and weak* convergence, and proved some properties. By RNS_Real Mizar functor, real normed spaces as real number spaces already defined in the article [18],...

Weak orthogonality and weak property ( β ) in some Banach sequence spaces

Yunan Cui, Henryk Hudzik, Ryszard Płuciennik (1999)

Czechoslovak Mathematical Journal

It is proved that a Köthe sequence space is weakly orthogonal if and only if it is order continuous. Criteria for weak property ( β ) in Orlicz sequence spaces in the case of the Luxemburg norm as well as the Orlicz norm are given.

Weakly continuous functions of Baire class 1.

T. S. S. R. K. Rao (2000)

Extracta Mathematicae

For a compact Hausdorff space K and a Banach space X, let WC(K,X) denote the space of X-valued functions defined on K, that are continuous when X has the weak topology. In this note by a simple Banach space theoretic argument, we show that given f belonging to WC(K,X) there exists a net {fa} contained in C(K,X) (space of norm continuous functions) such that fa --> f pointwise w.r.t. the norm topology on X. Such a function f is said to be of Baire class 1.

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