zbMATH — the first resource for mathematics

Examples
Geometry Search for the term Geometry in any field. Queries are case-independent.
Funct* Wildcard queries are specified by * (e.g. functions, functorial, etc.). Otherwise the search is exact.
"Topological group" Phrases (multi-words) should be set in "straight quotation marks".
au: Bourbaki & ti: Algebra Search for author and title. The and-operator & is default and can be omitted.
Chebyshev | Tschebyscheff The or-operator | allows to search for Chebyshev or Tschebyscheff.
"Quasi* map*" py: 1989 The resulting documents have publication year 1989.
so: Eur* J* Mat* Soc* cc: 14 Search for publications in a particular source with a Mathematics Subject Classification code (cc) in 14.
"Partial diff* eq*" ! elliptic The not-operator ! eliminates all results containing the word elliptic.
dt: b & au: Hilbert The document type is set to books; alternatively: j for journal articles, a for book articles.
py: 2000-2015 cc: (94A | 11T) Number ranges are accepted. Terms can be grouped within (parentheses).
la: chinese Find documents in a given language. ISO 639-1 language codes can also be used.

Operators
a & b logic and
a | b logic or
!ab logic not
abc* right wildcard
"ab c" phrase
(ab c) parentheses
Fields
any anywhere an internal document identifier
au author, editor ai internal author identifier
ti title la language
so source ab review, abstract
py publication year rv reviewer
cc MSC code ut uncontrolled term
dt document type (j: journal article; b: book; a: book article)
Roots of contractions with Hilbert-Schmidt defect operator and C ·0 completely non-unitary part. (English) Zbl 0885.47007
Summary: Let T be a controller on a separable complex Hilbert space such that T is a coupling of a normal and a C 10 contraction. If A is an mth root of T, where A has Hilbert-Schmidt defect operator, then there exists a nilpotent operator O m acting on a finite-dimensional Hilbert space, a normal contraction N, a unilateral shift U, a quasi-affinity Z and an operator X of trace class such that |ZA-(O m NU)Z| 1 =|0|X|| 1 . Here |·| 1 denotes the trace norm. If also the spectrum of A is a subset of the reals, then A is similar to the direct sum of a nilpotent O m and a self-adjoint contraction M. It is shown that if a contraction T has Hilbert-Schmidt defect operator and is either dominant or injective k-quasihyponormal or p-hyponormal (0<p<1) or k-paranormal (with reducing normal subspaces) or reductive (G 1 ) with C ·0 completely non-unitary part, then T is a coupling of the above type.
MSC:
47B20Subnormal operators, hyponormal operators, etc.
47A45Canonical models for contractions and nonselfadjoint operators