Separable Space

2014 ◽  
Author(s):  
Stamatis Cambanis
Keyword(s):  
Separable Space

Projections on Tree-Like banach Spaces

1985 ◽  
Vol 37 (5) ◽  
pp. 908-920
Author(s):  
A. D. Andrew
Keyword(s):  
Banach Space ◽  
Linear Operator ◽  
Banach Spaces ◽  
Bounded Linear Operator ◽  
Unconditional Basis ◽  
Reflexive Banach Space ◽  
Separable Space ◽  
Bounded Linear ◽  
Tree Space

1. In this paper, we investigate the ranges of projections on certain Banach spaces of functions defined on a diadic tree. The notion of a “tree-like” Banach space is due to James 4], who used it to construct the separable space JT which has nonseparable dual and yet does not contain l1. This idea has proved useful. In [3], Hagler constructed a hereditarily c0 tree space, HT, and Schechtman [6] constructed, for each 1 ≦ p ≦ ∞, a reflexive Banach space, STp with a 1-unconditional basis which does not contain lp yet is uniformly isomorphic to for each n.In [1] we showed that if U is a bounded linear operator on JT, then there exists a subspace W ⊂ JT, isomorphic to JT such that either U or (1 — U) acts as an isomorphism on W and UW or (1 — U)W is complemented in JT. In this paper, we establish this result for the Hagler and Schechtman tree spaces.

On the Topology of a Two-Parameter, Non-Metric and Non-Separable Space. I

1937 ◽  
Vol 38 (1) ◽  
pp. 204
Author(s):  
Edgar Graham Harrell
Keyword(s):  
Separable Space ◽  
Two Parameter

Separable Topological Space of Hereditary

NUTA Journal ◽  
2020 ◽  
Vol 7 (1-2) ◽  
pp. 68-70
Author(s):  
Raj Narayan Yadav ◽  
Bed Prasad Regmi ◽  
Surendra Raj Pathak
Keyword(s):  
Topological Space ◽  
Topological Property ◽  
Sufficient Condition ◽  
Topological Properties ◽  
Necessary And Sufficient Condition ◽  
Separable Space ◽  
Separable Topological Space ◽  
Necessary And Sufficient

A property of a topological space is termed hereditary ifand only if every subspace of a space with the property also has the property. The purpose of this article is to prove that the topological property of separable space is hereditary. In this paper we determine some topological properties which are hereditary and investigate necessary and sufficient condition functions for sub-spaces to possess properties of sub-spaces which are not in general hereditary.

Batch process modeling by using temporal feature and Gaussian mixture model

2019 ◽  
Vol 42 (6) ◽  
pp. 1204-1214
Author(s):  
Wei Guo ◽  
Tianhong Pan ◽  
Zhengming Li ◽  
Shan Chen
Keyword(s):  
Gaussian Mixture Model ◽  
Mixture Model ◽  
Batch Process ◽  
Gaussian Mixture ◽  
Batch Processes ◽  
Separable Space ◽  
Temporal Features ◽  
Learning Techniques ◽  
Multi Phase ◽  
Work First

Multi-model/multi-phase modeling algorithm has been widely used to monitor the product quality in complicated batch processes. Most multi-model/ multi-phase modeling methods hinge on the structure of a linearly separable space or a combination of different sub-spaces. However, it is impossible to accurately separate the overlapping region samples into different operating sub-spaces using unsupervised learning techniques. A Gaussian mixture model (GMM) using temporal features is proposed in the work. First, the number of sub-model is estimated by using the maximum interval process trend analysis algorithm. Then, the GMM parameters constrained with the temporal value are identified by using the expectation maximization (EM) algorithm, which minimizes confusion in overlapping regions of different Gaussian processes. A numerical example and a penicillin fermentation process demonstrate the effectiveness of the proposed algorithm.

Sense and sidedness in the graphics pipeline via a passage through a separable space

2008 ◽  
Vol 25 (4) ◽  
pp. 367-375
Author(s):  
Sherif Ghali
Keyword(s):  
Separable Space

Continuity properties in constructive mathematics

1992 ◽  
Vol 57 (2) ◽  
pp. 557-565 ◽  
Author(s):  
Hajime Ishihara
Keyword(s):  
Continuous Mapping ◽  
Constructive Mathematics ◽  
Separable Space ◽  
Continuity Properties

AbstractThe purpose of this paper is an axiomatic study of the interrelations between certain continuity properties. We deal with principles which are equivalent to the statements “every mapping is sequentially nondiscontinuous”, “every sequentially nondiscontinuous mapping is sequentially continuous”, and “every sequentially continuous mapping is continuous”. As corollaries, we show that every mapping of a complete separable space is continuous in constructive recursive mathematics (the Kreisel-Lacombe-Schoenfield-Tsejtin theorem) and in intuitionism.

scholarly journals Orthogonality in normed spaces

1986 ◽  
Vol 33 (3) ◽  
pp. 449-455 ◽  
Author(s):  
J. R. Partington
Keyword(s):  
Euclidean Space ◽  
Normed Space ◽  
Product Space ◽  
Inner Product Space ◽  
Inner Product ◽  
Normed Spaces ◽  
Separable Space ◽  
Orthogonality In Normed Spaces

Some properties which different definitions or orthogonality in a normed space can possess are considered. It is shown that orthogonality can be defined on any separable space with many of the properties possessed by the usual orthogonality in an inner-product space, but that the possession of a further property forces the space to be isomorphic to a Euclidean space.

scholarly journals Sequential separability vs selective sequential separability

Filomat ◽  
2015 ◽  
Vol 29 (1) ◽  
pp. 121-124 ◽  
Author(s):  
Angelo Bella ◽  
Camillo Costantini
Keyword(s):  
Separable Space

A space X is sequentially separable if there is a countable D ? X such that every point of X is the limit of a sequence of points from D. We present two examples of a sequentially separable space which is not selectively sequentially separable. One of them is in addition countable and sequential.

scholarly journals Generators of reflexive algebras

1975 ◽  
Vol 20 (2) ◽  
pp. 159-164
Author(s):  
W. E. Longstaff
Keyword(s):  
Hilbert Space ◽  
Von Neumann Algebra ◽  
Complex Hilbert Space ◽  
Bounded Operators ◽  
Finitely Generated ◽  
Separable Space ◽  
Von Neumann ◽  
Underlying Space ◽  
Weakly Closed ◽  
Reflexive Algebras

For any collection of closed subspaces of a complex Hilbert space the set of bounded operators that leave invariant all the members of the collection is a weakly-closed algebra. The class of such algebras is precisely the class of reflexive algebras as defined for example in Radjavi and Rosenthal (1969) and contains the class of von Neumann algebras.In this paper we consider the problem of when such algebras are finitely generated as weakly-closed algebras. It is to be hoped that analysis of this problem may shed some light on the famous unsolved problem of whether every von Neumann algebra on a separable Hilbert space is finitely generated. The case where the underlying space is separable and the collection of subspaces is totally ordered is dealt with in Longstaff (1974). In the present paper the result of Longstaff (1974) is generalized to the case of a direct product of countably many totally ordered collections each on a separable space. Also a method of obtaining non-finitely generated reflexive algebras is given.

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