EXCISION IN CYCLIC TYPE HOMOLOGY OF FRÉCHET ALGEBRAS

2001 ◽  
Vol 33 (3) ◽  
pp. 283-291 ◽  
Author(s):  
JACEK BRODZKI ◽  
ZINAIDA A. LYKOVA
Keyword(s):  
Approximate Identity ◽  
Excision Property ◽  
Pure Extension ◽  
Cyclic Type

It is proved that every topologically pure extension of Fréchet algebras 0 → I → A → A/I → 0 such that I is strongly H-unital has the excision property in continuous (co)homology of the following types: bar, naive-Hochschild, Hochschild, cyclic, and periodic cyclic. In particular, the property holds for every extension of Fréchet algebras such that I has a left or right bounded approximate identity.

scholarly journals Existence of the Solutions of Nonlinear Fractional Differential Equations Using the Fixed Point Technique in Extended b-Metric Spaces

Symmetry ◽  
2021 ◽  
Vol 13 (2) ◽  
pp. 158
Author(s):  
Liliana Guran ◽  
Monica-Felicia Bota
Keyword(s):  
Fixed Point ◽  
Metric Spaces ◽  
Boundary Value ◽  
Fixed Point Problem ◽  
Point Problem ◽  
Existence Of A Solution ◽  
Shadowing Property ◽  
Limit Shadowing ◽  
Type Boundary ◽  
Cyclic Type

The purpose of this paper is to prove fixed point theorems for cyclic-type operators in extended b-metric spaces. The well-posedness of the fixed point problem and limit shadowing property are also discussed. Some examples are given in order to support our results, and the last part of the paper considers some applications of the main results. The first part of this section is devoted to the study of the existence of a solution to the boundary value problem. In the second part of this section, we study the existence of solutions to fractional boundary value problems with integral-type boundary conditions in the frame of some Caputo-type fractional operators.

scholarly journals Production of a single cyclic type of fructooligosaccharide structure by inulin‐degrading Paenibacillus sp. LX 16 newly isolated from Jerusalem artichoke root

2016 ◽  
Vol 9 (3) ◽  
pp. 419-429 ◽  
Author(s):  
Zhihua Yao ◽  
Jiqiang Guo ◽  
Wenzhu Tang ◽  
Zhen Sun ◽  
Yingmin Hou ◽  
...  
Keyword(s):  
Jerusalem Artichoke ◽  
Paenibacillus Sp ◽  
Cyclic Type

scholarly journals The convolution algebraH1(R)

2010 ◽  
Vol 8 (2) ◽  
pp. 167-179 ◽  
Author(s):  
R. L. Johnson ◽  
C. R. Warner
Keyword(s):  
Banach Algebra ◽  
Maximal Ideal ◽  
Tauberian Theorem ◽  
Singular Integrals ◽  
Approximate Identity ◽  
Maximal Ideal Space ◽  
Ideal Space

H1(R) is a Banach algebra which has better mapping properties under singular integrals thanL1(R) . We show that its approximate identity sequences are unbounded by constructing one unbounded approximate identity sequence {vn}. We introduce a Banach algebraQthat properly lies betweenH1andL1, and use it to show thatc(1 + lnn) ≤ ||vn||H1≤Cn1/2. We identify the maximal ideal space ofH1and give the appropriate version of Wiener's Tauberian theorem.

scholarly journals A class of factorable topological algebras

1990 ◽  
Vol 33 (1) ◽  
pp. 53-59 ◽  
Author(s):  
E. Ansari-Piri
Keyword(s):  
Vector Space ◽  
Topological Vector Space ◽  
Approximate Identity ◽  
Necessary Condition ◽  
Topological Algebras ◽  
Approximate Identities ◽  
Cohen Factorization ◽  
Locally Convex ◽  
Space Property ◽  
Uniformly Bounded

The famous Cohen factorization theorem, which says that every Banach algebra with bounded approximate identity factors, has already been generalized to locally convex algebras with what may be termed “uniformly bounded approximate identities”. Here we introduce a new notion, that of fundamentality generalizing both local boundedness and local convexity, and we show that a fundamental Fréchet algebra with uniformly bounded approximate identity factors. Fundamentality is a topological vector space property rather than an algebra property. We exhibit some non-fundamental topological vector space and give a necessary condition for Orlicz space to be fundamental.

The excision theorems in Hochschild and cyclic homologies

2014 ◽  
Vol 144 (2) ◽  
pp. 305-317
Author(s):  
Guram Donadze ◽  
Manuel Ladra
Keyword(s):  
Hochschild Homology ◽  
Excision Property ◽  
Crossed Modules ◽  
Simplicial Algebras

We study the excision property for Hochschild and cyclic homologies in the category of simplicial algebras. We extend Wodzicki's notion of H-unital algebras to simplicial algebras and then show that a simplicial algebra I* satisfies excision in Hochschild and cyclic homologies if and only if it is H-unital. We use this result in the category of crossed modules of algebras and provide an answer to the question posed in the recent paper by Donadze et al. We also give (based on work by Guccione and Guccione) the excision theorem in Hochschild homology with coefficients.

Constructing pure injective hulls

1980 ◽  
Vol 45 (3) ◽  
pp. 544-548 ◽  
Author(s):  
Wilfrid Hodges
Keyword(s):  
Abelian Group ◽  
Homomorphic Image ◽  
Injective Hull ◽  
Pure Extension ◽  
The One ◽  
Injective Hulls

Let A be an abelian group and B a pure injective pure extension of A. Then there is a homomorphic image C of B over A which is a pure injective hull of A; C can be constructed by using Zorn's lemma to find a suitable congruence on B. In a paper [4] which greatly generalises this and related facts about pure injectives, Walter Taylor asks (Problem 1.5) whether one can find a “construction” of C which is more concrete than the one mentioned above; he asks also whether the points of C can be explicitly described. In this note I return the answer No.

Theoretical Analyses of the Universal Approximation Capability of a Class of Higher Order Neural Networks Based on Approximate Identity

2016 ◽  
pp. 1456-1470 ◽  
Author(s):  
Saeed Panahian Fard ◽  
Zarita Zainuddin
Keyword(s):  
Neural Networks ◽  
Approximation Theory ◽  
Special Class ◽  
Higher Order ◽  
Approximate Identity ◽  
Universal Approximation ◽  
Multivariate Functions ◽  
Higher Order Neural Networks ◽  
Approximation Capability ◽  
Theoretical Analyses

One of the most important problems in the theory of approximation functions by means of neural networks is universal approximation capability of neural networks. In this study, we investigate the theoretical analyses of the universal approximation capability of a special class of three layer feedforward higher order neural networks based on the concept of approximate identity in the space of continuous multivariate functions. Moreover, we present theoretical analyses of the universal approximation capability of the networks in the spaces of Lebesgue integrable multivariate functions. The methods used in proving our results are based on the concepts of convolution and epsilon-net. The obtained results can be seen as an attempt towards the development of approximation theory by means of neural networks.

Operator Algebras with Contractive Approximate Identities

1994 ◽  
Vol 46 (2) ◽  
pp. 397-414 ◽  
Author(s):  
Yiu-Tung Poon ◽  
Zhong-Jin Ruan
Keyword(s):  
Operator Algebra ◽  
Operator Algebras ◽  
Banach Algebras ◽  
Approximate Identity ◽  
The Other ◽  
Double Centralizer ◽  
Approximate Identities ◽  
Centralizer Algebras ◽  
Matrix Norms ◽  
Centralizer Algebra

AbstractWe study operator algebras with contractive approximate identities and their double centralizer algebras. These operator algebras can be characterized as L∞- Banach algebras with contractive approximate identities. We provide two examples, which show that given a non-unital operator algebra A with a contractive approximate identity, its double centralizer algebra M(A) may admit different operator algebra matrix norms, with which M(A) contains A as an M-ideal. On the other hand, we show that there is a unique operator algebra matrix norm on the unitalization algebra A1 of A such that A1 contains A as an M-ideal.

Positive Forms on Nuclear *-Algebras and Their Integral Representations

1990 ◽  
Vol 42 (3) ◽  
pp. 410-469 ◽  
Author(s):  
Alain Bélanger ◽  
Erik G. F. Thomas
Keyword(s):  
Integral Representation ◽  
Positive Cone ◽  
Approximate Identity ◽  
Integral Representations ◽  
Regularity Conditions ◽  
Direct Integral ◽  
Positive Form ◽  
Representations Of Algebras ◽  
Almost All ◽  
Order Intervals

Abstract.The main result of this paper establishes the existence and uniqueness of integral representations of KMS functionals on nuclear *- algebras. Our first result is about representations of *-algebras by means of operators having a common dense domain in a Hilbert space. We show, under certain regularity conditions, that (Powers) self-adjoint representations of a nuclear *-algebra, which admit a direct integral decomposition, disintegrate into representations which are almost all self-adjoint. We then define and study the class of self-derivative algebras. All algebras with an identity are in this class and many other examples are given. We show that if is a self-derivative algebra with an equicontinuous approximate identity, the cone of all positive forms on is isomorphic to the cone of all positive invariant kernels on These in turn correspond bijectively to the invariant Hilbert subspaces of the dual space This shows that if is a nuclear -space, the positive cone of has bounded order intervals, which implies that each positive form on has an integral representation in terms of the extreme generators of the cone. Given a continuous exponentially bounded one-parameter group of *-automorphisms of we can define the subcone of all invariant positive forms satisfying the KMS condition. Central functionals can be viewed as KMS functionals with respect to a trivial group action. Assuming that is a self-derivative algebra with an equicontinuous approximate identity, we show that the face generated by a self-adjoint KMS functional is a lattice. If is moreover a nuclear *-algebra the previous results together imply that each self-adjoint KMS functional has a unique integral representation by means of extreme KMS functionals almost all of which are self-adjoint.

Ideals of the Quantum Group Algebra, Arens Regularity and Weakly Compact Multipliers

2020 ◽  
Vol 63 (4) ◽  
pp. 825-836
Author(s):  
Mehdi Nemati ◽  
Maryam Rajaei Rizi
Keyword(s):  
Quantum Group ◽  
Group Algebra ◽  
Approximate Identity ◽  
Compact Quantum Group ◽  
Closed Ideal ◽  
Locally Compact ◽  
Weakly Compact ◽  
Locally Compact Quantum Group ◽  
Arens Regularity ◽  
Second Dual

AbstractLet $\mathbb{G}$ be a locally compact quantum group and let $I$ be a closed ideal of $L^{1}(\mathbb{G})$ with $y|_{I}\neq 0$ for some $y\in \text{sp}(L^{1}(\mathbb{G}))$. In this paper, we give a characterization for compactness of $\mathbb{G}$ in terms of the existence of a weakly compact left or right multiplier $T$ on $I$ with $T(f)(y|_{I})\neq 0$ for some $f\in I$. Using this, we prove that $I$ is an ideal in its second dual if and only if $\mathbb{G}$ is compact. We also study Arens regularity of $I$ whenever it has a bounded left approximate identity. Finally, we obtain some characterizations for amenability of $\mathbb{G}$ in terms of the existence of some $I$-module homomorphisms on $I^{\ast \ast }$ and on $I^{\ast }$.

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