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We give a brief review of holomorphic motions and its relation with quasiconformal mapping theory. Furthermore, we apply the holomorphic motions to give new proofs of famous Konig's Theorem and Bottcher's Theorem in classical complex…

We study properties of continuous semi-homogeneous operators of degree $k$ via various functions (e.g. measures of noncompactness) on all bounded subsets of a Banach space. We prove necessary and sufficient conditions for these functions to…

We study almost Hermitian 4-manifolds with holonomy algebra, for the canonical Hermitian connection, of dimension at most one. We show how Riemannian 4-manifolds admitting five orthonormal symplectic forms fit therein and classify them. In…

The authors lay the foundations for the study of normal families of holomorphic functions and mappings on an infinite-dimensional normed linear space. Characterizations of normal families, in terms of value distribution, spherical…

In this paper, we investigate classes of Lip-linear operators constructed using the composition ideal method. We focus on two fundamental linear operator ideals, $p$-summing and strongly $p$-summing operators, and extend them to define the…

This paper presents a solution to a problem from superanalysis about the existence of Hilbert-Banach superalgebras. Two main results are derived: 1) There exist Hilbert norms on some graded algebras (infinite-dimensional superalgebras…

Two different notions of approximate Birkhoff-James orthogonality in nor\-med linear spaces have been introduced by Dragomir and Chmie\-li\'n\-ski. In the present paper we consider a global and a local approximate symmetry of the…

The idea of best approximation in linear n-normed space is presented and some examples showing various possibilities of best approximations in linear n-normed space is given. Also, we study strictly convex n-norm and enquire about the…

In this note we prove new coincidence results for multiple summing mappings, related to the cotypes of the Banach spaces involved.

It is well known in Banach space theory that for a finite dimensional space $E$ there exists a constant $c_E$, such that for all sequences $(x_k)_k \subset E$ one has \[ \summ_k \noo x_k \rrm \kl c_E \pl \sup_{\eps_k \pm 1} \noo \summ_k…

We introduce and study two new relations between function spaces over measure spaces of infinite measure, motivated by the question of establishing compactness. The first relation captures the uniform decay of function (quasi-)norms ``at…

The class of absolutely norming operators on complex Hilbert spaces of arbitrary dimensions was introduced in [6] and a spectral characterization theorem for these operators was established in [11]. In this paper we extend the concept of…

It is proved, that if an almost Hermitian manifold satisfies the axiom of coholomorphic spheres, it is conformal flat.

It is proved that the relation of isomorphism between separable Banach spaces is a complete analytic equivalence relation, i.e., that any analytic equivalence relation Borel reduces to it. Thus, separable Banach spaces up to isomorphism…

We prove a substantial extension of a well-known result due to Bennett and Carl: The inclusion of a 2-concave symmetric Banach sequence space E into l_2 is (E,1)-summing, i.e. for every unconditionally summable sequence (x_n) in E the…

We prove the asymptotic equivalence of three sequences of ideal norms associated with the UMD-property of Banach spaces.

In [3] S. J. Bhatt and H. V. Dedania exposed certain classes of Banach algebras in which every element is a topological divisor of zero. We identify a new (large) class of Banach algebras with the aforementioned property, namely, the class…

In this article we describe all possible infinite linear configurations that can be found in a shift of any set of positive upper Banach density. This simultaneously generalizes Szemer\'edi's theorem on arithmetic progressions and the…

The category $Ban$ of Banach spaces and linear maps of norm $\leq 1$ is locally $\aleph_1$-presentable but not locally finitely presentable. We prove, however, that $Ban$ is locally finitely presentable in the enriched sense over complete…

For each ideal of multilinear mappings $\cal M$ we explicitly construct a corresponding ideal $^{a}{\cal M}$ such that multilinear forms in $^{a}{\cal M}$ are exactly those which can be approximated, in the uniform norm, by multilinear…