On spectrally bounded linear maps on B(X)

2020 ◽  
Vol 490 (1) ◽  
pp. 124206
Author(s):  
Constantin Costara
Keyword(s):  
Bounded Linear ◽  
Linear Maps ◽  
Spectrally Bounded

scholarly journals The spectrally bounded linear maps on operator algebras

2002 ◽  
Vol 150 (3) ◽  
pp. 261-271 ◽  
Author(s):  
Jianlian Cui ◽  
Jinchuan Hou
Keyword(s):  
Operator Algebras ◽  
Bounded Linear ◽  
Linear Maps ◽  
Spectrally Bounded

Spectrally Bounded Linear Maps on 𝓑(X)

2004 ◽  
Vol 47 (3) ◽  
pp. 369-372 ◽  
Author(s):  
Ajda Fošner ◽  
Peter Šemrl
Keyword(s):  
Bounded Linear ◽  
Linear Maps ◽  
Spectrally Bounded ◽  
Bounded Below

AbstractWe characterize surjective linear maps on that are spectrally bounded and spectrally bounded below.

scholarly journals Essentially spectrally bounded linear maps

2009 ◽  
Vol 137 (10) ◽  
pp. 3329-3329 ◽  
Author(s):  
M. Bendaoud ◽  
A. Bourhim
Keyword(s):  
Bounded Linear ◽  
Linear Maps ◽  
Spectrally Bounded

scholarly journals Locally spectrally bounded linear maps

2011 ◽  
Vol 136 (1) ◽  
pp. 81-89 ◽  
Author(s):  
M. Bendaoud ◽  
M. Sarih
Keyword(s):  
Bounded Linear ◽  
Linear Maps ◽  
Spectrally Bounded

scholarly journals A Completely Bounded Noncommutative Choquet Boundary for Operator Spaces

2017 ◽  
Vol 2019 (22) ◽  
pp. 6819-6886 ◽  
Author(s):  
Raphaël Clouâtre ◽  
Christopher Ramsey
Keyword(s):  
Structural Properties ◽  
Extension Property ◽  
Operator Space ◽  
Operator Spaces ◽  
Unique Extension ◽  
Bounded Linear ◽  
C Algebra ◽  
Choquet Boundary ◽  
Linear Maps ◽  
Contractive Maps

Abstract We develop a completely bounded counterpart to the noncommutative Choquet boundary of an operator space. We show how the class of completely bounded linear maps is too large to accommodate our purposes. To overcome this obstacle, we isolate the subset of completely bounded linear maps admitting a dilation of the same norm that is multiplicative on the associated C*-algebra. We view such maps as analogs of the familiar unital completely contractive maps, and we exhibit many of their structural properties. Of particular interest to us are those maps that are extremal with respect to a natural dilation order. We establish the existence of extremals and show that they have a certain unique extension property. In particular, they give rise to *-homomorphisms that we use to associate to any representation of an operator space an entire scale of C*-envelopes. We conjecture that these C*-envelopes are all *-isomorphic and verify this in some important cases.

Preduals and Nuclear Operators Associated with Bounded, p-Convex, p-Concave and Positive p-Summing Operators

2007 ◽  
Vol 59 (3) ◽  
pp. 614-637 ◽  
Author(s):  
C. C. A. Labuschagne
Keyword(s):  
Banach Spaces ◽  
Positive Operators ◽  
Banach Lattices ◽  
Bounded Operators ◽  
Bounded Linear ◽  
Nuclear Operators ◽  
Linear Maps

AbstractWe use Krivine's form of the Grothendieck inequality to renorm the space of bounded linear maps acting between Banach lattices. We construct preduals and describe the nuclear operators associated with these preduals for this renormed space of bounded operators as well as for the spaces of p-convex, p-concave and positive p-summing operators acting between Banach lattices and Banach spaces. The nuclear operators obtained are described in terms of factorizations through classical Banach spaces via positive operators.

Conditions under which all the bounded linear maps are compact

1965 ◽  
Vol 158 (1) ◽  
pp. 1-5 ◽  
Author(s):  
Elton Lacey ◽  
R. J. Whitley
Keyword(s):  
Bounded Linear ◽  
Linear Maps
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