Sums of characteristic values of compact polynomial operator pencils
نویسندگان
چکیده
منابع مشابه
On variations of characteristic values of entire matrix pencils
Entire matrix-valued functions of a complex argument (entire matrix pencils) are considered. Bounds for spectral variations of pencils are derived. In particular, approximations of entire pencils by polynomial pencils are investigated. Our results are new even for polynomial pencils. © 2005 Elsevier Inc. All rights reserved.
متن کاملHow to Compare the Absolute Values of Operator Sums and the Sums of Absolute Values?
We address the problem of comparing |A+B| and |A|+ |B| , for A,B ∈Mn(C) . Some results are obtained by using a technique of positive linear maps and several open questions are proposed. Mathematics subject classification (2010): Primary 15A60, 47A30, 47A60.
متن کاملReductions of operator pencils
We study problems associated with an operator pencil, i.e., a pair of operators on Banach spaces. Two natural problems to consider are linear constrained differential equations and the description of the generalized spectrum. The main tool to tackle either of those problems is the reduction of the pencil. There are two kinds of natural reduction operations associated to a pencil, which are conj...
متن کاملOn the Characteristic Polynomial of the Almost Mathieu Operator
Let Aθ be the rotation C*-algebra for angle θ. For θ = p/q with p and q relatively prime, Aθ is the sub-C*-algebra of Mq(C(T )) generated by a pair of unitaries u and v satisfying uv = e2πiθvu. Let hθ,λ = u+u +λ/2(v+ v) be the almost Mathieu operator. By proving an identity of rational functions we show that for q even, the constant term in the characteristic polynomial of hθ,λ is (−1) q/2(1 + ...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Journal of Mathematical Analysis and Applications
سال: 2008
ISSN: 0022-247X
DOI: 10.1016/j.jmaa.2007.05.043