On the Structure of Certain Nest Algebra Modules

1987 ◽  
Vol 39 (6) ◽  
pp. 1405-1412
Author(s):  
G. J. Knowles
Keyword(s):  
Operator Algebras ◽  
Adjoint Operator ◽  
Systematic Investigation ◽  
Unique Determination ◽  
Nest Algebra ◽  
Minimal Elements ◽  
Open Questions ◽  
Weakly Closed ◽  
Order Homomorphisms

Let be a nest algebra of operators on some Hilbert space H. Weakly closed -modules were first studied by J. Erdos and S. Power in [4]. It became apparent that many interesting classes of non self-adjoint operator algebras arise as just such a module. This paper undertakes a systematic investigation of the correspondence which arises between such modules and order homomorphisms from Lat into itself. This perspective provides a basis to answer some open questions arising from [4]. In particular, the questions concerning unique “determination” and characterization of maximal and minimal elements under this correspondence, are resolved. This is then used to establish when the determining homomorphism is unique.

Generators of Nest Algebras

1974 ◽  
Vol 26 (3) ◽  
pp. 565-575 ◽  
Author(s):  
W. E. Longstaff
Keyword(s):  
Hilbert Space ◽  
Separable Hilbert Space ◽  
Linear Operators ◽  
Nest Algebra ◽  
Bounded Linear Operators ◽  
Bounded Linear ◽  
Closed Algebra ◽  
Nest Algebras ◽  
Weakly Closed

A collection of subspaces of a Hilbert space is called a nest if it is totally ordered by inclusion. The set of all bounded linear operators leaving invariant each member of a given nest forms a weakly-closed algebra, called a nest algebra. Nest algebras were introduced by J. R. Ringrose in [9]. The present paper is concerned with generating nest algebras as weakly-closed algebras, and in particular with the following question which was first raised by H. Radjavi and P. Rosenthal in [8], viz: Is every nest algebra on a separable Hilbert space generated, as a weakly-closed algebra, by two operators? That the answer to this question is affirmative is proved by first reducing the problem using the main result of [8] and then by using a characterization of nests due to J. A. Erdos [2].

Perturbation of a nest algebra module

1983 ◽  
Vol 93 (2) ◽  
pp. 303-306 ◽  
Author(s):  
Sotirios Karanasios
Keyword(s):  
General Situation ◽  
Compact Perturbation ◽  
Nest Algebra ◽  
Nest Algebras ◽  
Weakly Closed ◽  
Carry Over ◽  
Algebra Module ◽  
Algebra Of Operators

Fall, Arveson and Muhly(4) characterized the compact perturbation of nest algebras. In fact they proved that the compact perturbation of a nest algebra corresponding to a nest of projections is the algebra of operators which are quasitriangular relative to this nest. Erdos and Power(3) investigated weakly closed ideals and modules of nest algebras and these exhibit properties that are very close to the properties of the nest algebras themselves. They also showed that in certain cases, as in the case when the homomorphism which determines the nest algebra module is continuous, the results of Fall, Arveson and Muhly carry over to the more general situation. In this paper we provide a characterization of the compact perturbation of any nest algebra module.

scholarly journals Hyers-Ulam-Rassias stability of (m, n)-Jordan derivations

2020 ◽  
Vol 18 (1) ◽  
pp. 1615-1624
Author(s):  
Guangyu An ◽  
Ying Yao
Keyword(s):  
Operator Algebras ◽  
Adjoint Operator ◽  
Rassias Stability

Abstract In this paper, we study the Hyers-Ulam-Rassias stability of ( m , n ) (m,n) -Jordan derivations. As applications, we characterize ( m , n ) (m,n) -Jordan derivations on C ⁎ {C}^{\ast } -algebras and some non-self-adjoint operator algebras.

Systematic discovery and characterization of stress-related microRNA genes in Oryza sativa

Biologia ◽  
2015 ◽  
Vol 70 (1) ◽  
Author(s):  
Kai Bin Xie ◽  
Xue Zhou ◽  
Tian Hai Zhang ◽  
Bao Long Zhang ◽  
Li Ming Chen ◽  
...  
Keyword(s):  
Abiotic Stress ◽  
Stress Responses ◽  
Systematic Investigation ◽  
Chemical Toxicity ◽  
Promoter Regions ◽  
Crop Species ◽  
Translation Inhibition ◽  
Microrna Genes ◽  
Insight Into

AbstractAbiotic stresses including drought, salinity, extreme temperatures, chemical toxicity and oxidative are the natural status of the environment to exert serious threats to agriculture. Abiotic stress-related microRNAs (ASmiRNAs) are a group of microRNAs (miRNAs) regulating stress responses in plants. However, the systematic investigation of ASmiRNAs is limited in Rice (O. sativa), a typical abiotic stress-resistant crop species. In the present work, we systematically investigated ASmiRNAs in silico. First, we identified 177 putative ASmiRNAs in O.sativa. Second, we found most ASmiRNAs were driven by TATA-promoter and most stress-related miRNA promoter regions contained the stress-related elements. Third, we found many ASmiRNAs families were species/family specific and a set of miRNAs might derive from genomic repeat-sequences in O. sativa. Finally, we found the ASmiRNAs in O. sativa target 289 genes with 1050 predicted target sites in which 98% sites have cleavage activity and 2% sites have translation inhibition activity. In conclusion, our findings provide an insight into both the function and evolution of ASmiRNAs and improve our understanding on the mechanism of abiotic stress resistance in O. sativa.

Amalgamated duplication of the Banach algebra 𝔄 along a 𝔄-bimodule 𝒜

2018 ◽  
Vol 17 (09) ◽  
pp. 1850169 ◽  
Author(s):  
Hossein Javanshiri ◽  
Mehdi Nemati
Keyword(s):  
Banach Algebra ◽  
Cohomology Group ◽  
Banach Algebras ◽  
Multiplier Algebra ◽  
Topological Center ◽  
Maximal Ideals ◽  
Open Questions ◽  
Arens Regularity ◽  
Amalgamated Duplication

Let [Formula: see text] and [Formula: see text] be Banach algebras such that [Formula: see text] is a Banach [Formula: see text]-bimodule with compatible actions. We define the product [Formula: see text], which is a strongly splitting Banach algebra extension of [Formula: see text] by [Formula: see text]. After characterization of the multiplier algebra, topological center, (maximal) ideals and spectrum of [Formula: see text], we restrict our investigation to the study of semisimplicity, regularity, Arens regularity of [Formula: see text] in relation to that of the algebras [Formula: see text], [Formula: see text] and the action of [Formula: see text] on [Formula: see text]. We also compute the first cohomology group [Formula: see text] for all [Formula: see text] as well as the first-order cyclic cohomology group [Formula: see text], where [Formula: see text] is the [Formula: see text]th dual space of [Formula: see text] when [Formula: see text] and [Formula: see text] itself when [Formula: see text]. These results are not only of interest in their own right, but also they pave the way for obtaining some new results for Lau products and module extensions of Banach algebras as well as triangular Banach algebra. Finally, special attention is devoted to the cyclic and [Formula: see text]-weak amenability of [Formula: see text]. In this context, several open questions arise.

Application of Atom Probe Microanalysis for Understanding Microstructure Evolution in Nickel Base Superalloy Welds

2000 ◽  
Vol 6 (S2) ◽  
pp. 350-351
Author(s):  
S. S. Babu ◽  
S. A. David ◽  
M. K. Miller
Keyword(s):  
Microstructure Evolution ◽  
Predictive Models ◽  
Strong Relationship ◽  
Atom Probe ◽  
Systematic Investigation ◽  
Nickel Base Superalloy ◽  
Cooling Conditions ◽  
Nickel Base ◽  
Base Superalloy

The characterization of the microstructure evolution during welding of nickel base superalloys is required for efficient reuse and reclamation of used and failed components. Previous atom probe analysis of electron-beam and laser-beam welds revealed complex alloying elemental partitioning between the γ and γ phases. Rapid cooling conditions in the weld leads to non-equilibrium partitioning and large amplitude Cr and Co levels in the γ phase. These results indicated that there is a strong relationship between weld cooling rate and the precipitation of γ′ precipitates from the γ phase. To understand and develop predictive models, a systematic investigation of the microstructure evolution in CM247DS alloy under controlled thermomechanical conditions are being performed. This paper describes some recent results on the elemental partitioning between γ and γ′ phases obtained with atom probe microanalysis.

scholarly journals Characterization of linear maps onMnwhose multiplicity maps have maximal norm, with an application in quantum information

Quantum ◽  
2018 ◽  
Vol 2 ◽  
pp. 51
Author(s):  
Daniel Puzzuoli
Keyword(s):  
Quantum Information ◽  
Quantum Channel ◽  
Operator Algebras ◽  
Optimal Performance ◽  
Single Shot ◽  
Trace Norm ◽  
Linear Maps ◽  
The Family ◽  
Matrix Transposition

Given a linear mapΦ:Mn→Mm, its multiplicity maps are defined as the family of linear mapsΦ⊗idk:Mn⊗Mk→Mm⊗Mk, whereidkdenotes the identity onMk. Let‖⋅‖1denote the trace-norm on matrices, as well as the induced trace-norm on linear maps of matrices, i.e.‖Φ‖1=max{‖Φ(X)‖1:X∈Mn,‖X‖1=1}. A fact of fundamental importance in both operator algebras and quantum information is that‖Φ⊗idk‖1can grow withk. In general, the rate of growth is bounded by‖Φ⊗idk‖1≤k‖Φ‖1, and matrix transposition is the canonical example of a map achieving this bound. We prove that, up to an equivalence, the transpose is the unique map achieving this bound. The equivalence is given in terms of complete trace-norm isometries, and the proof relies on a particular characterization of complete trace-norm isometries regarding preservation of certain multiplication relations.We use this result to characterize the set of single-shot quantum channel discrimination games satisfying a norm relation that, operationally, implies that the game can be won with certainty using entanglement, but is hard to win without entanglement. Specifically, we show that the well-known example of such a game, involving the Werner-Holevo channels, is essentially the unique game satisfying this norm relation. This constitutes a step towards a characterization of single-shot quantum channel discrimination games with maximal gap between optimal performance of entangled and unentangled strategies.

On Operator Algebras and Invariant Subspaces

1969 ◽  
Vol 21 ◽  
pp. 1178-1181 ◽  
Author(s):  
Chandler Davis ◽  
Heydar Radjavi ◽  
Peter Rosenthal
Keyword(s):  
Hilbert Space ◽  
Elementary Proof ◽  
Operator Algebras ◽  
Equivalent Form ◽  
Invariant Subspaces ◽  
Complex Hilbert Space ◽  
Closed Algebra ◽  
Weakly Closed ◽  
Special Case

If is a collection of operators on the complex Hilbert space , then the lattice of all subspaces of which are invariant under every operator in is denoted by Lat . An algebra of operators on is defined (3; 4) to be reflexive if for every operator B on the inclusion Lat ⊆ Lat B implies .Arveson (1) has proved the following theorem. (The abbreviation “m.a.s.a.” stands for “maximal abelian self-adjoint algebra”.)ARVESON's THEOREM. Ifis a weakly closed algebra which contains an m.a.s.a.y and if Lat, then is the algebra of all operators on .A generalization of Arveson's Theorem was given in (3). Another generalization is Theorem 2 below, an equivalent form of which is Corollary 3. This theorem was motivated by the following very elementary proof of a special case of Arveson's Theorem.

scholarly journals Synthesis and Characterization of Acridinium Dyes for Photoredox Catalysis

Synlett ◽  
2019 ◽  
Vol 30 (07) ◽  
pp. 827-832 ◽  
Author(s):  
Alexander White ◽  
Leifeng Wang ◽  
David Nicewicz
Keyword(s):  
Photophysical Properties ◽  
Direct Conversion ◽  
Systematic Investigation ◽  
Synthetic Methods ◽  
Synthesis And Characterization ◽  
Substitution Effects ◽  
Photoredox Catalysis ◽  
Methods Development

Photoredox catalysis is a rapidly evolving platform for synthetic methods development. The prominent use of acridinium salts as a sustainable option for photoredox catalysts has driven the development of more robust and synthetically useful versions based on this scaffold. However, more complicated syntheses, increased cost, and limited commercial availability have hindered the adoption of these catalysts by the greater synthetic community. By utilizing the direct conversion of a xanthylium salt into the corresponding acridinium as the key transformation, we present an efficient and scalable preparation of the most synthetically useful acridinium reported to date. This divergent strategy also enabled the preparation of a suite of novel acridinium dyes, allowing for a systematic investigation of substitution effects on their photophysical properties.

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