Special Classes of Bounded Operators

2003 ◽  
pp. 293-312
Author(s):  
Philippe Blanchard ◽  
Erwin Brüning
Keyword(s):  
Bounded Operators ◽  
Special Classes

scholarly journals Operator Symbols and Operator Indices

Symmetry ◽  
2019 ◽  
Vol 12 (1) ◽  
pp. 64
Author(s):  
Vladimir Vasilyev
Keyword(s):  
Banach Spaces ◽  
Differential Operators ◽  
Index Theorem ◽  
Symbolic Calculus ◽  
Smooth Manifolds ◽  
Bounded Operators ◽  
Pseudo Differential Operators ◽  
Operator Symbols ◽  
Special Classes

We suggest a certain variant of symbolic calculus for special classes of linear bounded operators acting in Banach spaces. According to the calculus we formulate an index theorem and give applications to elliptic pseudo-differential operators on smooth manifolds with non-smooth boundaries.

scholarly journals Products of Positive Operators

2021 ◽  
Vol 15 (2) ◽  
Author(s):  
Maximiliano Contino ◽  
Michael A. Dritschel ◽  
Alejandra Maestripieri ◽  
Stefania Marcantognini
Keyword(s):  
Positive Operator ◽  
Hilbert Spaces ◽  
Spectral Properties ◽  
Compact Operators ◽  
Positive Operators ◽  
Bounded Operators ◽  
Infinite Dimensional ◽  
Finite Dimensional ◽  
Special Classes

AbstractOn finite dimensional spaces, it is apparent that an operator is the product of two positive operators if and only if it is similar to a positive operator. Here, the class $${\mathcal {L}^{+\,2}}$$ L + 2 of bounded operators on separable infinite dimensional Hilbert spaces which can be written as the product of two bounded positive operators is studied. The structure is much richer, and connects (but is not equivalent to) quasi-similarity and quasi-affinity to a positive operator. The spectral properties of operators in $${\mathcal {L}^{+\,2}}$$ L + 2 are developed, and membership in $${\mathcal {L}^{+\,2}}$$ L + 2 among special classes, including algebraic and compact operators, is examined.

Organization in the School Dental Service. 9. Special classes of patients

BDJ ◽  
1971 ◽  
Vol 131 (9) ◽  
pp. 417-418
Author(s):  
G Turner
Keyword(s):  
Dental Service ◽  
Special Classes

scholarly journals The dual of the space of bounded operators on a Banach space

2021 ◽  
Vol 8 (1) ◽  
pp. 48-59
Author(s):  
Fernanda Botelho ◽  
Richard J. Fleming
Keyword(s):  
Banach Space ◽  
Tensor Product ◽  
Banach Spaces ◽  
Dual Space ◽  
Tensor Products ◽  
Bounded Operators ◽  
Projective Tensor Product ◽  
Projective Tensor

Abstract Given Banach spaces X and Y, we ask about the dual space of the 𝒧(X, Y). This paper surveys results on tensor products of Banach spaces with the main objective of describing the dual of spaces of bounded operators. In several cases and under a variety of assumptions on X and Y, the answer can best be given as the projective tensor product of X ** and Y *.

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