A New Class of Maximal Triangular Algebras

2018 ◽  
Vol 61 (4) ◽  
pp. 909-931
Author(s):  
John Lindsay Orr
Keyword(s):  
Finite Multiplicity ◽  
Asymptotic Structure ◽  
C Algebras ◽  
New Class ◽  
Related Family ◽  
Infinite Multiplicity ◽  
Triangular Algebras

AbstractTriangular algebras, and maximal triangular algebras in particular, have been objects of interest for over 50 years. Rich families of examples have been studied in the context of many w*- and C*-algebras, but there remains a dearth of concrete examples in $B({\cal H})$. In previous work, we described a family of maximal triangular algebras of finite multiplicity. Here, we investigate a related family of maximal triangular algebras with infinite multiplicity, and unearth a new asymptotic structure exhibited by these algebras.

scholarly journals L q-solutions to the Cosserat spectrum in bounded and exterior domains

Analysis ◽  
2006 ◽  
Vol 26 (1) ◽  
Author(s):  
Stephan Weyers
Keyword(s):  
Accumulation Point ◽  
Exterior Domains ◽  
Finite Multiplicity ◽  
Cosserat Spectrum ◽  
Infinite Multiplicity

SummaryIfλ = 1 is an eigenvalue of infinite multiplicity and λ = 2 is an accumulation point of eigenvalues of finite multiplicity. For the

Symmetrically Completely Bounded Linear Maps Between C*-Algebras

1992 ◽  
Vol 35 (2) ◽  
pp. 278-286
Author(s):  
Wai-Shing Tang
Keyword(s):  
Hilbert Space ◽  
Representation Theorem ◽  
Linear Subspace ◽  
Linear Operators ◽  
Bounded Linear Operators ◽  
Bounded Linear ◽  
C Algebras ◽  
New Class ◽  
Linear Maps

AbstractWe study the properties of a new class SCB(L, B) of bounded linear maps, called symmetrically completely bounded maps, from a linear subspace L of a C* -algebra to another C*-algebra B. This class contains the class of all completely bounded linear maps from L to B. In particular, we obtain a representation theorem for maps in SCB(L, B) when B is the algebra of all bounded linear operators on a Hilbert space.

Some results for a class of extended centralizers on C∗-algebras

2020 ◽  
Vol 12 (06) ◽  
pp. 2050087
Author(s):  
Anamika Sarma ◽  
Nilakshi Goswami ◽  
Vishnu Narayan Mishra
Keyword(s):  
C Algebras ◽  
New Class

The aim of this paper is to introduce a new class of generalized centralizers on [Formula: see text]-algebras which is termed as extended [Formula: see text]-centralizer. We study different properties of this class of centralizers. Moreover, we define a class of [Formula: see text]-algebras which contains the prime [Formula: see text]-algebras as a subclass. Different properties of extended centralizers with respect to this class of [Formula: see text]-algebras are discussed with suitable examples.

A note on nonmultidimensional superstable theories

1985 ◽  
Vol 50 (4) ◽  
pp. 1020-1024 ◽  
Author(s):  
Anand Pillay ◽  
Charles Steinhorn
Keyword(s):  
Stability Theory ◽  
Saturated Model ◽  
Sufficient Condition ◽  
Finite Multiplicity ◽  
Superstable Theory ◽  
Superstable Theories ◽  
Infinite Multiplicity ◽  
Countable Structure

In this paper we prove that if T is the complete elementary diagram of a countable structure and is a theory as in the title, then Vaught's conjecture holds for T. This result is Theorem 7, below. In the process of establishing this proposition, in Theorem 3 we give a sufficient condition for a superstable theory having only countably many types without parameters to be ω-stable. Familiarity with the rudiments of stability theory, as presented in [3] and [4], will be supposed throughout. The notation used is, by now, standard.We begin by giving a new proof of a lemma due to J. Saffe in [6]. For T stable, recall that the multiplicity of a type p over a set A ⊆ ℳ ⊨ T is the cardinality of the collection of strong types over A extending p.Lemma 1 (Saffe). Let T be stable, A ⊆ ℳ ⊨ T. If t(b̄, A) has infinite multiplicity and t(c̄, A) has finite multiplicity, then t(b̄, A ∪ {c̄}) has infinite multiplicity.Proof. We suppose not and work for a contradiction. Let ‹b̄γ:γ ≤ α›, α ≥ ω, be a list of elements so that t(b̄γ, A) = t(b̄, A) for all γ ≤ α, and st(b̄γ, A) ≠ st(b̄δ, A) for γ ≠ δ. Furthermore, let c̄γ satisfy t(b̄γ∧c̄γ, A) = t(b̄ ∧ c̄, A) for each γ < α.Since t(c̄, A) has finite multiplicity, we may assume for all γ, δ < α. that st(c̄γ, A) = st(c̄δ, A). For each γ < α there is an automorphism fγ of the so-called “monster model” of T (a sufficiently large, saturated model of T) that preserves strong types over A and is such that f(c̄γ) = c̄0.

On the spectrum of the periodic Dirac operator

1981 ◽  
Vol 89 (1-2) ◽  
pp. 55-62 ◽  
Author(s):  
B. J. Harris
Keyword(s):  
Dirac Operator ◽  
Spectral Gap ◽  
Dirac Operators ◽  
Finite Multiplicity ◽  
Infinite Multiplicity ◽  
Periodic Dirac Operator

SynopsisIn an earlier paper we considered periodic Dirac operators and obtained criteria for them to be self-adjoint and for their spectra to be devoid of eigenvalues of finite multiplicity. The question of the existence of eigenvalues of infinite multiplicity was left open. In this article we obtain further criteria for self-adjointness and show that under these conditions periodic Dirac operators do not possess eigenvalues of infinite multiplicity. We also obtain a spectral gap result.

Obstructions for semigroups of partial isometries to be self-adjoint

2016 ◽  
Vol 161 (1) ◽  
pp. 107-116
Author(s):  
JANEZ BERNIK ◽  
ALEXEY I. POPOV
Keyword(s):  
Hilbert Space ◽  
Von Neumann Algebra ◽  
Separable Hilbert Space ◽  
Finite Multiplicity ◽  
Partial Isometries ◽  
Von Neumann ◽  
Infinite Multiplicity ◽  
Complex Separable Hilbert Space

AbstractIn this paper we study the following question: given a semigroup ${\mathcal S}$ of partial isometries acting on a complex separable Hilbert space, when does the selfadjoint semigroup ${\mathcal T}$ generated by ${\mathcal S}$ again consist of partial isometries? It has been shown by Bernik, Marcoux, Popov and Radjavi that the answer is positive if the von Neumann algebra generated by the initial and final projections corresponding to the members of ${\mathcal S}$ is abelian and has finite multiplicity. In this paper we study the remaining case of when this von Neumann algebra has infinite multiplicity and show that, in a sense, the answer in this case is generically negative.

In Situ microscopy of the anodic etching of silicon

1995 ◽  
Vol 53 ◽  
pp. 232-233
Author(s):  
Frances M. Ross ◽  
Peter C. Searson
Keyword(s):  
Composite Structures ◽  
High Surface ◽  
High Surface Area ◽  
Chemical Properties ◽  
Selective Etching ◽  
Silicon On Insulator ◽  
Second Phase ◽  
Porous Layers ◽  
New Class ◽  
Porous Semiconductors

Porous semiconductors represent a relatively new class of materials formed by the selective etching of a single or polycrystalline substrate. Although porous silicon has received considerable attention due to its novel optical properties1, porous layers can be formed in other semiconductors such as GaAs and GaP. These materials are characterised by very high surface area and by electrical, optical and chemical properties that may differ considerably from bulk. The properties depend on the pore morphology, which can be controlled by adjusting the processing conditions and the dopant concentration. A number of novel structures can be fabricated using selective etching. For example, self-supporting membranes can be made by growing pores through a wafer, films with modulated pore structure can be fabricated by varying the applied potential during growth, composite structures can be prepared by depositing a second phase into the pores and silicon-on-insulator structures can be formed by oxidising a buried porous layer. In all these applications the ability to grow nanostructures controllably is critical.

The microtubule associated protein (MAP) tau forms a new class of triple-stranded left-hand helical fibrous protein polymer

1992 ◽  
Vol 50 (1) ◽  
pp. 540-541
Author(s):  
G. C. Ruben ◽  
K. Iqbal ◽  
I. Grundke-Iqbal ◽  
H. Wisniewski ◽  
T. L. Ciardelli ◽  
...  
Keyword(s):  
Axial Ratio ◽  
Normal Structure ◽  
Paired Helical Filaments ◽  
Left Hand ◽  
New Class ◽  
Protein Polymer ◽  
Fibrous Protein ◽  
Protein Map ◽  
Neurotransmitter Transport ◽  
Alzheimer Neurofibrillary Tangles

In neurons, the microtubule associated protein, tau, is found in the axons. Tau stabilizes the microtubules required for neurotransmitter transport to the axonal terminal. Since tau has been found in both Alzheimer neurofibrillary tangles (NFT) and in paired helical filaments (PHF), the study of tau's normal structure had to preceed TEM studies of NFT and PHF. The structure of tau was first studied by ultracentrifugation. This work suggested that it was a rod shaped molecule with an axial ratio of 20:1. More recently, paraciystals of phosphorylated and nonphosphoiylated tau have been reported. Phosphorylated tau was 90-95 nm in length and 3-6 nm in diameter where as nonphosphorylated tau was 69-75 nm in length. A shorter length of 30 nm was reported for undamaged tau indicating that it is an extremely flexible molecule. Tau was also studied in relation to microtubules, and its length was found to be 56.1±14.1 nm.

Study of segregation in La1.8Sr0.2CuO4 superconductor by STEM-EDS microanalysis

1987 ◽  
Vol 45 ◽  
pp. 54-55
Author(s):  
T. F. Kelly ◽  
P. J. Lee ◽  
E. E. Hellstrom ◽  
D. C. Larbalestier
Keyword(s):  
Rare Earth ◽  
High Field ◽  
Transport Current ◽  
Total Thickness ◽  
New Class ◽  
Ceramic Superconductors ◽  
Current Densities ◽  
Group Ii ◽  
Eds Microanalysis

Recently there has been much excitement over a new class of high Tc (>30 K) ceramic superconductors of the form A1-xBxCuO4-x, where A is a rare earth and B is from Group II. Unfortunately these materials have only been able to support small transport current densities 1-10 A/cm2. It is very desirable to increase these values by 2 to 3 orders of magnitude for useful high field applications. The reason for these small transport currents is as yet unknown. Evidence has, however, been presented for superconducting clusters on a 50-100 nm scale and on a 1-3 μm scale. We therefore planned a detailed TEM and STEM microanalysis study in order to see whether any evidence for the clusters could be seen.A La1.8Sr0.2Cu04 pellet was cut into 1 mm thick slices from which 3 mm discs were cut. The discs were subsequently mechanically ground to 100 μm total thickness and dimpled to 20 μm thickness at the center.

Electronic structure studies of conducting polymers by electron energy-loss spectroscopy

1996 ◽  
Vol 54 ◽  
pp. 160-161
Author(s):  
J. Fink
Keyword(s):  
Electronic Structure ◽  
Conducting Polymers ◽  
Conjugated Polymers ◽  
Electron Acceptors ◽  
Electron Donors ◽  
Light Emitting ◽  
One Dimensional ◽  
New Class ◽  
Electrical Conductivities ◽  
Electron Energy Loss

Conducting polymers comprises a new class of materials achieving electrical conductivities which rival those of the best metals. The parent compounds (conjugated polymers) are quasi-one-dimensional semiconductors. These polymers can be doped by electron acceptors or electron donors. The prototype of these materials is polyacetylene (PA). There are various other conjugated polymers such as polyparaphenylene, polyphenylenevinylene, polypoyrrole or polythiophene. The doped systems, i.e. the conducting polymers, have intersting potential technological applications such as replacement of conventional metals in electronic shielding and antistatic equipment, rechargable batteries, and flexible light emitting diodes.Although these systems have been investigated almost 20 years, the electronic structure of the doped metallic systems is not clear and even the reason for the gap in undoped semiconducting systems is under discussion.

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