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This four-day workshop is devoted to discuss advanced topics from commutative algebra and Banach space theory. The theme of this workshop is twofold: parallel series of lectures will be delivered in c...
Metric Dynamical System Let be a probability space. Let be a metric dynamical system: (i) (ii) (iii) preserves th...
We present a reflexive Banach space $\mathfrak{X}_{_{^\text{usm}}}$ which is Hereditarily Indecomposable and satisfies the following properties. In every subspace $Y$ of $\mathfrak{X}_{_{^\text{usm}}}...
We study the homogeneous equation (*) $ u' = \Delta u$, $t > 0$, $u(0)=f\in wX$, where $wX$ is a weighted Banach space, $w(x)= (1+||x||)^k$, $x\in \r^n$ with $k\ge 0$, $ \Delta$ is the Laplacian, $Y$ ...
Abstract: In this note a large class of primary Banach spaces is characterized. Namely, it will be demonstrated that under the Continuum Hypothesis the ultrapower of any infinite dimensional nonsuperr...
Abstract: In this paper it will be shown that assuming the Continuum Hypothesis (CH) every nonreflexive Banach space ultrapower is isometrically isomorphic to the space of continuous, bounded and real...
It is shown that variants of the HI methods could yield objects closely connected to the classical Banach spaces. Thus we present a new c0 saturated space, denoted as X0,with rather tight structure.
Under the assumption that c is a regular cardinal, we prove the existence and uniqueness of a Boolean algebra B of size c defined by sharing the main structural properties that P(!)/fin has under CH a...
In this paper, we introduce a new Halpern type iterative sequence for a countable family of nonexpansive mappings. Then we prove that such a sequence converges strongly to a common fixed point of a co...
We discuss the connection between the expansion of small sets in graphs, and the Schatten norms of their adjacency matrix. In conjunction with a variant of the Azuma inequality for uniformly smooth no...
In this study, we provide a new Kantorovich-type convergence theorem for Newton’s method in Banach space. Its condition is different from earlier ones, and therefore it has theoretical and practical v...
We study the sufficient and necessary conditions of the convergence for parameter-based rational methods in a Banach space. We derive a closed form of error bounds in terms of a real parameter $\l...

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