A characterization of upper triangular trace class matrices

2009 ◽  
Vol 347 (1-2) ◽  
pp. 59-62 ◽  
Author(s):  
Nicolae Popa
Keyword(s):  
Trace Class

scholarly journals An inverse spectral problem for a star graph of Krein strings

2016 ◽  
Vol 2016 (715) ◽  
Author(s):  
Jonathan Eckhardt
Keyword(s):  
Spectral Problem ◽  
Spectral Data ◽  
Inverse Spectral Problem ◽  
Trace Class ◽  
Star Graph ◽  
Borel Measures ◽  
Inverse Spectral ◽  
The Individual

AbstractWe solve an inverse spectral problem for a star graph of Krein strings, where the known spectral data comprises the spectrum associated with the whole graph, the spectra associated with the individual edges as well as so-called coupling matrices. In particular, we show that these spectral quantities uniquely determine the weight within the class of Borel measures on the graph, which give rise to trace class resolvents. Furthermore, we obtain a concise characterization of all possible spectral data for this class of weights.

ON THE DOMAIN OF SINGULAR TRACES

2002 ◽  
Vol 13 (06) ◽  
pp. 667-674 ◽  
Author(s):  
DANIELE GUIDO ◽  
TOMMASO ISOLA
Keyword(s):  
Positive Operator ◽  
Trace Class ◽  
Regular Operator ◽  
Infinite Rank

The question whether an operator belongs to the domain of some singular trace is addressed, together with the dual question whether an operator does not belong to the domain of some singular trace. We show that the answers are positive in general, namely for any (compact, infinite rank) positive operator A we exhibit two singular traces, the first being zero and the second being infinite on A. However, if we assume that the singular traces are genrated by a "regular" operator, the answers change, namely such traces alway vanish on trace-class, non singularly traceable operators and are always infinite on non trace-class, non singularly traceable operators. These results are achieved on a general semifinite factor and make use of a new characterization of singular traceability (cf. [7]).

scholarly journals Pseudo-differential operators on homogeneous spaces of compact and Hausdorff groups

2019 ◽  
Vol 31 (2) ◽  
pp. 275-282 ◽  
Author(s):  
Vishvesh Kumar
Keyword(s):  
Homogeneous Space ◽  
Closed Subgroup ◽  
Differential Operators ◽  
Homogeneous Spaces ◽  
Trace Class ◽  
Necessary And Sufficient Condition ◽  
Pseudo Differential Operators ◽  
Hausdorff Group ◽  
Necessary And Sufficient

AbstractLet G be a compact Hausdorff group and let H be a closed subgroup of G. We introduce pseudo-differential operators with symbols on the homogeneous space {G/H}. We present a necessary and sufficient condition on symbols for which these operators are in the class of Hilbert–Schmidt operators. We also give a characterization of and a trace formula for the trace class pseudo-differential operators on the homogeneous space {G/H}.

scholarly journals Characterization of the trace-class

1980 ◽  
Vol 78 (4) ◽  
pp. 545-545
Author(s):  
Parfeny P. Saworotnow
Keyword(s):  
Trace Class

scholarly journals A simple characterization of the trace-class of operators

1981 ◽  
Vol 4 (2) ◽  
pp. 411-412
Author(s):  
Parfeny P. Saworotnow
Keyword(s):  
Hilbert Space ◽  
Trace Class ◽  
Simple Characterization

The trace-class(τc)of operators on a Hilbert space is characterized in terms of existence of certain centralizers.

scholarly journals Range-Kernel Orthogonality and Elementary Operators: The Nonsmoothness Case

Complexity ◽  
2020 ◽  
Vol 2020 ◽  
pp. 1-7
Author(s):  
A. Bachir ◽  
A. Segres ◽  
Nawal Sayyaf
Keyword(s):  
Trace Class ◽  
Smooth Case ◽  
Counter Example ◽  
Elementary Operators ◽  
Trace Class Operators

The characterization of the points in C1ℋ, the trace class operators, that are orthogonal to the range of elementary operators has been carried out for certain kinds of elementary operators by many authors in the smooth case. In this note, we study that the characterization is a problem in nonsmoothness case for general elementary operators, and we give a counter example to S. Mecheri and M. Bounkhel results.

Morphological Characterization of Mycobacteriophage R1

1974 ◽  
Vol 32 ◽  
pp. 254-255
Author(s):  
B. L. Soloff ◽  
T. A. Rado
Keyword(s):  
Carbon Source ◽  
Stationary Phase ◽  
Growth Phase ◽  
Minimal Medium ◽  
Morphological Characterization ◽  
Logarithmic Growth Phase ◽  
Complete Lysis ◽  
Lysogenic Culture ◽  
Logarithmic Growth

Mycobacteriophage R1 was originally isolated from a lysogenic culture of M. butyricum. The virus was propagated on a leucine-requiring derivative of M. smegmatis, 607 leu−, isolated by nitrosoguanidine mutagenesis of typestrain ATCC 607. Growth was accomplished in a minimal medium containing glycerol and glucose as carbon source and enriched by the addition of 80 μg/ ml L-leucine. Bacteria in early logarithmic growth phase were infected with virus at a multiplicity of 5, and incubated with aeration for 8 hours. The partially lysed suspension was diluted 1:10 in growth medium and incubated for a further 8 hours. This permitted stationary phase cells to re-enter logarithmic growth and resulted in complete lysis of the culture.

AEM analysis of crystallization in Ti-based amorphous alloys

1983 ◽  
Vol 41 ◽  
pp. 270-271
Author(s):  
A.R. Pelton ◽  
A.F. Marshall ◽  
Y.S. Lee
Keyword(s):  
Magnetic Properties ◽  
Amorphous Alloys ◽  
Amorphous Materials ◽  
Isothermal Annealing ◽  
Amorphous Matrix ◽  
Nucleation And Growth ◽  
Current Interest ◽  
Amorphous Films ◽  
Electrical And Magnetic Properties

Amorphous materials are of current interest due to their desirable mechanical, electrical and magnetic properties. Furthermore, crystallizing amorphous alloys provides an avenue for discerning sequential and competitive phases thus allowing access to otherwise inaccessible crystalline structures. Previous studies have shown the benefits of using AEM to determine crystal structures and compositions of partially crystallized alloys. The present paper will discuss the AEM characterization of crystallized Cu-Ti and Ni-Ti amorphous films.Cu60Ti40: The amorphous alloy Cu60Ti40, when continuously heated, forms a simple intermediate, macrocrystalline phase which then transforms to the ordered, equilibrium Cu3Ti2 phase. However, contrary to what one would expect from kinetic considerations, isothermal annealing below the isochronal crystallization temperature results in direct nucleation and growth of Cu3Ti2 from the amorphous matrix.

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