Local and global equivalence of holomorphic operator functions of several variables

1980 ◽  
Vol 97 (1) ◽  
pp. 69-87
Author(s):  
Dieter Heunemann
Keyword(s):  
Several Variables ◽  
Holomorphic Operator ◽  
Operator Functions

scholarly journals Equivalence, linearization, and decomposition of holomorphic operator functions

1978 ◽  
Vol 28 (1) ◽  
pp. 102-144 ◽  
Author(s):  
I.C Gohberg ◽  
M.A Kaashoek ◽  
D.C Lay
Keyword(s):  
Holomorphic Operator ◽  
Operator Functions

scholarly journals MONOTONE TRACE FUNCTIONS OF SEVERAL VARIABLES

2005 ◽  
Vol 16 (07) ◽  
pp. 777-785 ◽  
Author(s):  
FRANK HANSEN
Keyword(s):  
Monotone Operator ◽  
Jensen’S Inequality ◽  
Matrix Functions ◽  
Jensen's Inequality ◽  
Expectation Values ◽  
C Algebra ◽  
Several Variables ◽  
Positive Elements ◽  
Operator Functions ◽  
Weak Majorization

We investigate monotone operator functions of several variables under a trace or a trace-like functional. In particular, we prove the inequality τ(x1⋯xn) ≤ τ(y1⋯yn) for a trace τ on a C*-algebra and abelian n-tuples (x1,…,xn) ≤ (y1,…,yn) of positive elements. We formulate and prove Jensen's inequality for expectation values, and we study matrix functions of several variables which are convex or monotone with respect to the weak majorization for matrices.

A class of holomorphic operator functions

1969 ◽  
Vol 5 (3) ◽  
pp. 212-216
Author(s):  
Yu L. Shmul'yan
Keyword(s):  
Holomorphic Operator ◽  
Operator Functions
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