Algebraic Formalism within the Works of Servois and its Influence on the Development of Linear Operator Theory

2012 ◽  
Author(s):  
Anthony J. Del Latto ◽  
Salvatore J. Petrilli, Jr.
Author(s):  
George W. Hanson ◽  
Alexander B. Yakovlev

1971 ◽  
Vol 12 (2) ◽  
pp. 110-117 ◽  
Author(s):  
P. A. Fillmore ◽  
J. P. Williams

The numerical range of a bounded linear operator A on a complex Hilbertspace H is the set W(A) = {(Af, f): ║f║ = 1}. Because it is convex andits closure contains the spectrum of A, the numerical range is often a useful toolin operator theory. However, even when H is two-dimensional, the numerical range of an operator can be large relative to its spectrum, so that knowledge of W(A) generally permits only crude information about A. P. R. Halmos [2] has suggested a refinement of the notion of numerical range by introducing the k-numerical rangesfor k = 1, 2, 3, …. It is clear that W1(A) = W(A). C. A. Berger [2] has shown that Wk(A) is convex.


2005 ◽  
Vol 22 (8) ◽  
pp. 1567 ◽  
Author(s):  
Derek S. Sabatke ◽  
Ann M. Locke ◽  
Robert W. McMillan ◽  
Eustace L. Dereniak

1965 ◽  
Vol 5 (1) ◽  
pp. 48-55
Author(s):  
W. Pranger

In this we will study analytic solutions to the linear functional equation where f and h are given functions, x is a given complex number and the function g is to be found. This is a generalization of Schröder's functional equation. The results obtained are global in nature and the solutions holomorphic. The equation will be viewed from the standpoint of linear operator theory. When studied in this manner one arrives at a general operator inversion formula.


1972 ◽  
Vol 36 (5) ◽  
pp. 388-407 ◽  
Author(s):  
N.W.A. Marsh ◽  
J.W.K. Chang ◽  
E. Rose

2010 ◽  
Vol 69 (1) ◽  
pp. 113-132 ◽  
Author(s):  
Marko Huhtanen ◽  
Santtu Ruotsalainen

Sign in / Sign up

Export Citation Format

Share Document