Ransford, Thomas (2006) On Pseudospectra and Power Growth. Technical Report. Unspecified. (Submitted)

PDF
160kB 
Abstract
The celebrated Kreiss matrix theorem is one of several results relating the norms of the powers of a matrix to its pseudospectra (i.e. the level curves of the norm of the resolvent). But to what extent do the pseudospectra actually determine the norms of the powers? Specifically, let be square matrices such that, with respect to the usual operator norm ,
(zIA)^=(zIB)^ (z).
Then it is known that . Are there similar bounds for for ? Does the answer change if are diagonalizable? What if holds, not just for the norm , but also for higherorder singular values? What if we use norms other than the usual operator norm? The answers to all these questions turn out to be negative, and in a rather strong sense.
The research was supported by grants from NSERC and the Canada Research Chairs program
Item Type:  Technical Report (Technical Report) 

Subjects:  H  N > Linear and multilinear algebra; matrix theory O  Z > Operator theory H  N > Numerical analysis 
Research Groups:  Numerical Analysis Group 
ID Code:  1119 
Deposited By:  Lotti Ekert 
Deposited On:  11 May 2011 09:56 
Last Modified:  29 May 2015 18:48 
Repository Staff Only: item control page