On the convexity of numerical range in quaternionic hilbert spaces

1984 ◽  
Vol 16 (1-4) ◽  
pp. 93-100 ◽  
Author(s):  
Yik-Hoi Au-Yeung
Keyword(s):  
Hilbert Spaces ◽  
Numerical Range

scholarly journals On the convexity of Stampfli's numerical range

1996 ◽  
Vol 53 (1) ◽  
pp. 33-37
Author(s):  
J. O. Agure
Keyword(s):  
Hilbert Spaces ◽  
Numerical Range

This paper investigates a certain type of numerical range introduced by Stampfli. In particular, we investigate the convexity of this set of elements of operators on Hilbert spaces and its relationship to the algebra numerical range implemented by elements of a W*-algebra.

On the Numerical Range of Compact Operators on Hilbert Spaces

1972 ◽  
Vol s2-5 (4) ◽  
pp. 704-706 ◽  
Author(s):  
G. de Barra ◽  
J. R. Giles ◽  
Brailey Sims
Keyword(s):  
Hilbert Spaces ◽  
Numerical Range ◽  
Compact Operators

The Numerical Range of 2-Dimensional Krein Space Operators

2008 ◽  
Vol 51 (1) ◽  
pp. 86-99 ◽  
Author(s):  
Hiroshi Nakazato ◽  
Natália Bebiano ◽  
João da Providência
Keyword(s):  
Hilbert Spaces ◽  
Numerical Range ◽  
Krein Space ◽  
Kreĭn Space

AbstractThe tracial numerical range of operators on a 2-dimensional Krein space is investigated. Results in the vein of those obtained in the context of Hilbert spaces are obtained.

A new method for approximation of closed convex subsets of B(H)

Filomat ◽  
2017 ◽  
Vol 31 (19) ◽  
pp. 6005-6013
Author(s):  
Mahdi Iranmanesh ◽  
Fatemeh Soleimany
Keyword(s):  
Best Approximation ◽  
Numerical Range ◽  
New Method ◽  
C Algebra ◽  
Convex Subsets

In this paper we use the concept of numerical range to characterize best approximation points in closed convex subsets of B(H): Finally by using this method we give also a useful characterization of best approximation in closed convex subsets of a C*-algebra A.

Unbounded Linear Operators

2018 ◽  
Author(s):  
D. E. Edmunds ◽  
W. D. Evans
Keyword(s):  
Hilbert Spaces ◽  
Linear Operators ◽  
Von Neumann ◽  
Limit Circle ◽  
Sectorial Operators ◽  
Closed Operators ◽  
The Stability ◽  
Symmetric Operators ◽  
Unbounded Linear Operators ◽  
Special Case

This chapter is concerned with closable and closed operators in Hilbert spaces, especially with the special classes of symmetric, J-symmetric, accretive and sectorial operators. The Stone–von Neumann theory of extensions of symmetric operators is treated as a special case of results for compatible adjoint pairs of closed operators. Also discussed in detail is the stability of closedness and self-adjointness under perturbations. The abstract results are applied to operators defined by second-order differential expressions, and Sims’ generalization of the Weyl limit-point, limit-circle characterization for symmetric expressions to J-symmetric expressions is proved.

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