arXiv subjects

A. Manoussakis

Publications and source records attributed to A. Manoussakis.

6 recordsLinked to original sources

arXiv2021

Variants of the James Tree space

Recently, W. Cuellar Carrera, N. de Rancourt, and V. Ferenczi introduced the notion of $d_2$-hereditarily indecomposable Banach spaces, i.e., non-Hilbertian spaces that do not contain the direct sum of any two non-Hilbertian subspaces. They posed the question of the existence of such spaces that are $\ell_2$-saturated. Motivated by this question, we define and study two variants $JT_{2,p}$ and $JT_G$ of the James Tree space $JT$. They are meant to be classical analogues of a future space that will affirmatively answer the aforementioned question.

math.FA↗

arXiv2016

An Indecomposable and unconditionally saturated Banach space

We construct an indecomposable reflexive Banach space $X_{ius}$ such that every infinite dimensional closed subspace contains an unconditional basic sequence. We also show that every operator $T\in \mathcal{B}(X_{ius})$ is of the form $λI+S$ with $S$ a strictly singular operator.

math.FA↗

arXiv2013

Types of tightness in spaces with unconditional basis

We present a reflexive Banach space with an unconditional basis which is quasi-minimal and tight by range, i.e. of type (4) in Ferenczi-Rosendal list within the framework of Gowers' classification program of Banach spaces, but contrary to the recently constructed space of type (4) also tight with constants, thus essentially extending the list of known examples in Gowers classification program. The space is defined on the base on a boundedly modified mixed Tsirelson space with use of a special coding function.

math.FA↗

arXiv2012

Function spaces not containing $\ell_{1}$

For $Ω$ bounded and open subset of $\mathbb{R}^{d_{0}}$ and $X$ a reflexive Banach space with 1-symmetric basis, the function space $JF_{X}(Ω)$ is defined. This class of spaces includes the classical James function space. Every member of this class is separable and has non-separable dual. We provide a proof of topological nature that $JF_{X}(Ω)$ does not contain an isomorphic copy of $\ell_{1}$. We also investigate the structure of these spaces and their duals.

math.FA↗

arXiv2006

A PMT-Block test bench

The front-end electronics of the ATLAS hadronic calorimeter (Tile Cal) is housed in a unit, called {\it PMT-Block}. The PMT-Block is a compact instrument comprising a light mixer, a PMT together with its divider and a {\it 3-in-1} card, which provides shaping, amplification and integration for the signals. This instrument needs to be qualified before being assembled on the detector. A PMT-Block test bench has been developed for this purpose. This test bench is a system which allows fast, albeit accurate enough, measurements of the main properties of a complete PMT-Block. The system, both hardware and software, and the protocol used for the PMT-Blocks characterisation are described in detail in this report. The results obtained in the test of about 10000 PMT-Blocks needed for the instrumentation of the ATLAS (LHC-CERN) hadronic Tile Calorimeter are also reported.

physics.ins-det↗

arXiv1997

Modified mixed Tsirelson spaces

We study the modified and boundedly modified mixed Tsirelson spaces $T_M[({\cal F}_{k_n},θ_n)_{n=1}^{\infty }]$ and $T_{M(s)}[({\cal F}_{k_n},θ_n)_{n=1}^{\infty }]$ respectively, defined by a subsequence $({\cal F}_{k_n})$ of the sequence of Schreier families $({\cal F}_n)$. These are reflexive asymptotic $\ell_1$ spaces with an unconditio- nal basis $(e_i)_i$ having the property that every sequence $\{ x_i\}_{i=1}^n$ of normalized disjointly supported vectors contained in $\langle e_i\rangle_{i=n}^{\infty }$ is equivalent to the basis of $\ell_1^n$. We show that if $\limθ_n^{1/n}=1$ then the space $T[({\cal F}_n,θ_n) _{n=1}^{\infty }]$ and its modified variations are totally incomparable by proving that $c_0$ is finitely disjointly representable in every block subspace of $T[({\cal F}_n, θ_n)_{n=1}^{\infty }]$. Next, we present an example of a boundedly modified mixed Tsirelson space $X_{M(1),u}$ which is arbitrarily distortable. Finally, we construct a variation of the space $X_{M(1),u}$ which is hereditarily indecomposable.

math.FA↗