Unitarily Invariant Operator Norms

1983 ◽  
Vol 35 (2) ◽  
pp. 274-299 ◽  
Author(s):  
C.-K. Fong ◽  
J. A. R. Holbrook
Keyword(s):  
Hilbert Space ◽  
Convex Functions ◽  
Invariant Operator ◽  
Space Operator ◽  
Numerical Radius ◽  
The Past ◽  
Operator Norms ◽  
Power Inequality ◽  
The Many ◽  
Image Position

1.1. Over the past 15 years there has grown up quite an extensive theory of operator norms related to the numerical radius1of a Hilbert space operator T. Among the many interesting developments, we may mention:(a) C. Berger's proof of the “power inequality”2(b) R. Bouldin's result that3for any isometry V commuting with T;(c) the unification by B. Sz.-Nagy and C. Foias, in their theory of ρ-dilations, of the Berger dilation for T with w(T) ≤ 1 and the earlier theory of strong unitary dilations (Nagy-dilations) for norm contractions;(d) the result by T. Ando and K. Nishio that the operator radii wρ(T) corresponding to the ρ-dilations of (c) are log-convex functions of ρ.

The power inequality on Banach spaces

1971 ◽  
Vol 69 (3) ◽  
pp. 411-415 ◽  
Author(s):  
Béla Bollobás
Keyword(s):  
Linear Operator ◽  
Banach Spaces ◽  
Normed Space ◽  
Bounded Linear Operator ◽  
Dual Space ◽  
Numerical Range ◽  
Numerical Radius ◽  
Bounded Linear ◽  
Power Inequality ◽  
Image Position

Let X be a complex normed space with dual space X′ and let T be a bounded linear operator on X. The numerical range of T is defined asand the numerical radius is v(T) = sup {|ν: νε V(T)}. Most known results and problems concerning numerical range can be found in the notes by Bonsall and Duncan (5).

scholarly journals A weaker condition for normality

1994 ◽  
Vol 36 (2) ◽  
pp. 249-253
Author(s):  
Ian Doust
Keyword(s):  
Hilbert Space ◽  
Orthogonal Projection ◽  
Operator Theory ◽  
Normal Operator ◽  
Borel Subset ◽  
Spectral Theorem ◽  
Space Operator ◽  
Countable Additivity ◽  
Normal Operators ◽  
Image Position

One of the most important results of operator theory is the spectral theorem for normal operators. This states that a normal operator (that is, a Hilbert space operator T such that T*T= TT*), can be represented as an integral with respect to a countably additive spectral measure,Here E is a measure that associates an orthogonal projection with each Borel subset of ℂ. The countable additivity of this measure means that if x Eℋ can be written as a sum of eigenvectors then this sum must converge unconditionally.

On Future Directions in Pathology

1982 ◽  
Vol 40 ◽  
pp. 274-277
Author(s):  
Benjamin F. Trump ◽  
Irene K. Berezesky ◽  
Raymond T. Jones
Keyword(s):  
Electron Microscopy ◽  
Transmission Electron Microscopy ◽  
Clinical Pathology ◽  
Future Directions ◽  
Diagnostic Pathology ◽  
The Past ◽  
Transmission Electron ◽  
Organ Systems ◽  
The Many

The role of electron microscopy and associated techniques is assured in diagnostic pathology. At the present time, most of the progress has been made on tissues examined by transmission electron microscopy (TEM) and correlated with light microscopy (LM) and by cytochemistry using both plastic and paraffin-embedded materials. As mentioned elsewhere in this symposium, this has revolutionized many fields of pathology including diagnostic, anatomic and clinical pathology. It began with the kidney; however, it has now been extended to most other organ systems and to tumor diagnosis in general. The results of the past few years tend to indicate the future directions and needs of this expanding field. Now, in addition to routine EM, pathologists have access to the many newly developed methods and instruments mentioned below which should aid considerably not only in diagnostic pathology but in investigative pathology as well.

A 200-Year History of the Study of Childhood Language Disorders of Unknown Origin: Changes in Terminology

2020 ◽  
Vol 5 (1) ◽  
pp. 6-11 ◽  
Author(s):  
Laurence B. Leonard
Keyword(s):  
Language Impairment ◽  
Specific Language Impairment ◽  
Scientific Literature ◽  
Language Disorder ◽  
Language Disorders ◽  
Unknown Origin ◽  
Developmental Language Disorder ◽  
The Past ◽  
History Of ◽  
The Many

Purpose The current “specific language impairment” and “developmental language disorder” discussion might lead to important changes in how we refer to children with language disorders of unknown origin. The field has seen other changes in terminology. This article reviews many of these changes. Method A literature review of previous clinical labels was conducted, and possible reasons for the changes in labels were identified. Results References to children with significant yet unexplained deficits in language ability have been part of the scientific literature since, at least, the early 1800s. Terms have changed from those with a neurological emphasis to those that do not imply a cause for the language disorder. Diagnostic criteria have become more explicit but have become, at certain points, too narrow to represent the wider range of children with language disorders of unknown origin. Conclusions The field was not well served by the many changes in terminology that have transpired in the past. A new label at this point must be accompanied by strong efforts to recruit its adoption by clinical speech-language pathologists and the general public.

The Many Pasts of Detective Fiction

2020 ◽  
Vol 1 (2) ◽  
pp. 157-172
Author(s):  
Thomas Leitch
Keyword(s):  
Detective Fiction ◽  
Golden Age ◽  
Public History ◽  
Detective Novel ◽  
Sherlock Holmes ◽  
Detective Story ◽  
The Past ◽  
Wide Range ◽  
Detective Novels ◽  
The Many

Building on Tzvetan Todorov's observation that the detective novel ‘contains not one but two stories: the story of the crime and the story of the investigation’, this essay argues that detective novels display a remarkably wide range of attitudes toward the several pasts they represent: the pasts of the crime, the community, the criminal, the detective, and public history. It traces a series of defining shifts in these attitudes through the evolution of five distinct subgenres of detective fiction: exploits of a Great Detective like Sherlock Holmes, Golden Age whodunits that pose as intellectual puzzles to be solved, hardboiled stories that invoke a distant past that the present both breaks with and echoes, police procedurals that unfold in an indefinitely extended present, and historical mysteries that nostalgically fetishize the past. It concludes with a brief consideration of genre readers’ own ambivalent phenomenological investment in the past, present, and future each detective story projects.

Law as a Field of Tension

2018 ◽  
Author(s):  
Andrea Gamberini
Keyword(s):  
Public Authority ◽  
The Public ◽  
The Past ◽  
Political Cultures ◽  
The Many

As it had been in the communal age, so, in the Visconti-Sforza era, law was the instrument that the public authority relied upon in order to subordinate the many actors present and to subjugate their political cultures. There is, therefore, the attempt to tighten a vice around competing powers—a vice that is at the same time legislative, doctrinal, and judicial. And yet, it is difficult to escape the impression of an effort whose outcomes were somewhat more uncertain than had been the case in the past. The chapter focuses on all these aspects of the deployment of legal and other stratagems to consolidate or to wrest power.

Evidence-based Assessment

2010 ◽  
pp. 76-98
Author(s):  
John Hunsley ◽  
Eric J. Mash
Keyword(s):  
Decision Making ◽  
Clinical Assessment ◽  
Assessment Process ◽  
Evidence Based ◽  
The Past ◽  
Specific Assessment ◽  
The Many ◽  
Selection Of ◽  
Made In

Evidence-based assessment relies on research and theory to inform the selection of constructs to be assessed for a specific assessment purpose, the methods and measures to be used in the assessment, and the manner in which the assessment process unfolds. An evidence-based approach to clinical assessment necessitates the recognition that, even when evidence-based instruments are used, the assessment process is a decision-making task in which hypotheses must be iteratively formulated and tested. In this chapter, we review (a) the progress that has been made in developing an evidence-based approach to clinical assessment in the past decade and (b) the many challenges that lie ahead if clinical assessment is to be truly evidence-based.

CPT-based liquefaction case histories compiled from three earthquakes in Canterbury, New Zealand

2021 ◽  
pp. 875529302199636
Author(s):  
Mertcan Geyin ◽  
Brett W Maurer ◽  
Brendon A Bradley ◽  
Russell A Green ◽  
Sjoerd van Ballegooy
Keyword(s):  
New Zealand ◽  
Case History ◽  
Prediction Models ◽  
Free Field ◽  
Case Histories ◽  
Cone Penetration ◽  
History Data ◽  
The Past ◽  
Surface Manifestation ◽  
The Many

Earthquakes occurring over the past decade in the Canterbury region of New Zealand have resulted in liquefaction case-history data of unprecedented quantity. This provides the profession with a unique opportunity to advance the prediction of liquefaction occurrence and consequences. Toward that end, this article presents a curated dataset containing ∼15,000 cone-penetration-test-based liquefaction case histories compiled from three earthquakes in Canterbury. The compiled, post-processed data are presented in a dense array structure, allowing researchers to easily access and analyze a wealth of information pertinent to free-field liquefaction response (i.e. triggering and surface manifestation). Research opportunities using these data include, but are not limited to, the training or testing of new and existing liquefaction-prediction models. The many methods used to obtain and process the case-history data are detailed herein, as is the structure of the compiled digital file. Finally, recommendations for analyzing the data are outlined, including nuances and limitations that users should carefully consider.

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