Superspaces of (s) with strong finite dimensional decomposition

1984 ◽  
Vol 42 (1) ◽  
pp. 58-66 ◽  
Author(s):  
Lasse Holmstr�m
Keyword(s):  
Finite Dimensional ◽  
Dimensional Decomposition ◽  
Finite Dimensional Decomposition

The finite-dimensional decomposition property in non-Archimedean Banach spaces

2014 ◽  
Vol 30 (11) ◽  
pp. 1833-1845
Author(s):  
Albert Kubzdela ◽  
Cristina Perez-Garcia
Keyword(s):  
Banach Spaces ◽  
Decomposition Property ◽  
Finite Dimensional ◽  
Dimensional Decomposition ◽  
Finite Dimensional Decomposition

scholarly journals Banach Spaces of Almost Universal Complemented Disposition

2019 ◽  
Vol 71 (1) ◽  
pp. 139-174
Author(s):  
Jesús M F Castillo ◽  
Yolanda Moreno
Keyword(s):  
Banach Space ◽  
Banach Spaces ◽  
Separable Banach Space ◽  
Complemented Subspace ◽  
Finite Dimensional ◽  
Dimensional Decomposition ◽  
Finite Dimensional Decomposition ◽  
Separable Spaces

Abstract We introduce and study the notion of space of almost universal complemented disposition (a.u.c.d.) as a generalization of Kadec space. We show that every Banach space with separable dual is isometrically contained as a $1$-complemented subspace of a separable a.u.c.d. space and that all a.u.c.d. spaces with $1$-finite dimensional decomposition (FDD) are isometric and contain isometric $1$-complemented copies of every separable Banach space with $1$-FDD. We then study spaces of universal complemented disposition (u.c.d.) and provide different constructions for such spaces. We also consider spaces of u.c.d. with respect to separable spaces.

scholarly journals The Complete Continuity Property and Finite Dimensional Decompositions

1995 ◽  
Vol 38 (2) ◽  
pp. 207-214
Author(s):  
Maria Girardi ◽  
William B. Johnson
Keyword(s):  
Banach Space ◽  
Local Structure ◽  
Continuity Property ◽  
Complete Continuity ◽  
Bounded Linear ◽  
Completely Continuous ◽  
Finite Dimensional ◽  
Dimensional Decomposition ◽  
Finite Dimensional Decomposition ◽  
Convergent Sequences

AbstractA Banach space has the complete continuity property (CCP) if each bounded linear operator from L1 into is completely continuous (i.e., maps weakly convergent sequences to norm convergent sequences). The main theorem shows that a Banach space failing the CCP has a subspace with a finite dimensional decomposition which fails the CCP. If furthermore the space has some nice local structure (such as fails cotype or is a lattice), then the decomposition may be strengthened to a basis.

Non-Linear Dynamics of Cardiovascular Variability Signals

1994 ◽  
Vol 33 (01) ◽  
pp. 81-84 ◽  
Author(s):  
S. Cerutti ◽  
S. Guzzetti ◽  
R. Parola ◽  
M.G. Signorini
Keyword(s):  
Dimensional Space ◽  
Severe Heart Failure ◽  
Parametric Models ◽  
Deterministic Systems ◽  
Finite Dimensional ◽  
Return Maps ◽  
Pathological Conditions ◽  
Non Linear ◽  
Space State

Abstract:Long-term regulation of beat-to-beat variability involves several different kinds of controls. A linear approach performed by parametric models enhances the short-term regulation of the autonomic nervous system. Some non-linear long-term regulation can be assessed by the chaotic deterministic approach applied to the beat-to-beat variability of the discrete RR-interval series, extracted from the ECG. For chaotic deterministic systems, trajectories of the state vector describe a strange attractor characterized by a fractal of dimension D. Signals are supposed to be generated by a deterministic and finite dimensional but non-linear dynamic system with trajectories in a multi-dimensional space-state. We estimated the fractal dimension through the Grassberger and Procaccia algorithm and Self-Similarity approaches of the 24-h heart-rate variability (HRV) signal in different physiological and pathological conditions such as severe heart failure, or after heart transplantation. State-space representations through Return Maps are also obtained. Differences between physiological and pathological cases have been assessed and generally a decrease in the system complexity is correlated to pathological conditions.

A closer look at the stable completion

2017 ◽  
Author(s):  
Ehud Hrushovski ◽  
François Loeser
Keyword(s):  
Inverse Limit ◽  
Unit Vector ◽  
Vector Spaces ◽  
Dimensional Vector ◽  
Compact Sets ◽  
Linear Topology ◽  
Topological Embedding ◽  
Definable Set ◽  
Finite Dimensional ◽  
The One

This chapter introduces the concept of stable completion and provides a concrete representation of unit vector Mathematical Double-Struck Capital A superscript n in terms of spaces of semi-lattices, with particular emphasis on the frontier between the definable and the topological categories. It begins by constructing a topological embedding of unit vector Mathematical Double-Struck Capital A superscript n into the inverse limit of a system of spaces of semi-lattices L(Hsubscript d) endowed with the linear topology, where Hsubscript d are finite-dimensional vector spaces. The description is extended to the projective setting. The linear topology is then related to the one induced by the finite level morphism L(Hsubscript d). The chapter also considers the condition that if a definable set in L(Hsubscript d) is an intersection of relatively compact sets, then it is itself relatively compact.

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