Analytic Renormings of C(K) Spaces

The aim of our present note is to show the strength of the existence of an equivalent analytic renorming of a Banach space, even compared to C∞-Fréchet smooth renormings. It was Haydon who first showed in [8] that C(K) spaces for K countable admit an equivalent C∞-Fréchet smooth norm. Later, in [7] and [9] he introduced a large clams of tree-like (uncountable) compacts K for which C(K) admits an equivalent C∞-Fréchet smooth norm. Recently, it was shown in [3] that C(K) spaces for K countable admit an equivalent analytic norm. Our Theorem 1 shows that in the class of C(K) spaces this result is the best possible.

A Characterization of Weakly Lindelöf Determined Banach Spaces

2000 Mathematics Subject Classification: 46B26, 46B03, 46B04.

On the Hyperbolicity Domain of the Polynomial x^n + a1x^(n-1) + 1/4+ an

∗ Partially supported by INTAS grant 97-1644

Nadel's Subschemes of Fano Manifolds X with a Picard Group Pic(X) Isomorphic to Z

∗The author supported by Contract NSFR MM 402/1994.

Partial Ovoids and Partial Spreads of Classical Finite Polar Spaces

2000 Mathematics Subject Classification: 05B25, 51E20.

Some properties of g- and P-spaces

A γ-space with a strictly positive measure is separable. An example of a non-separable γ−space with c.c.c. is given. A P−space with c.c.c. is countable and discrete.

Invariants of Unipotent Transformations Acting on Noetherian Relatively Free Algebras

2000 Mathematics Subject Classification: 16R10, 16R30.

Classification of the Maximal Subsemigroups of the Semigroup of all Partial Order-Preserving Transformations

Илинка А. Димитрова, Цветелина Н. Младенова - Моноида P Tn от всички частични преобразования върху едно n-елементно множество относно операцията композиция на преобразования е изучаван в различни аспекти от редица автори. Едно частично преобразование α се нарича запазващо наредбата, ако от x ≤ y следва, че xα ≤ yα за всяко x, y от дефиниционното множество на α. Обект на разглеждане в настоящата работа е моноида P On състоящ се от всички частични запазващи наредбата преобразования. Очевидно P On е под-моноид на P Tn. Направена е пълна класификация на максималните подполугрупи на моноида P On. Доказано е, че съществуват пет различни вида максимални подполугрупи на разглеждания моноид. Броят на всички максимални подполугрупи на POn е точно 2^n + 2n − 2.

About the Concept of Weights of WLTE(k) Estimators

2002 Mathematics Subject Classification: 62F35, 62F15.

Hausdorff Measures of Noncompactness and Interpolation Spaces

2000 Mathematics Subject Classification: 46B50, 46B70, 46G12.

On the Poisson Process of Order k Space

2010 Mathematics Subject Classification: 60E05, 62P05.