 About 37,100 results  books.google.com Likewise, we say that a cosemigroup (Tt)t>o on H is similar to a contraction
semigroup if there exists an invertible operator S £ B(H) such that iS 1lt«S < 1
for any t > 0. Clearly any T 6 B(H] similar to a contraction is power bounded, i.e., ... 

 books.google.com The generators of contraction semigroups are characterized by the classical
theorem of Lumer and Phillips, see for example [Pz, p. 14]. Recall that a
semigroup {etA}t>o is called a contraction semigroup if \\etA\\ < 1 for t > 0. For a
linear ... 

 books.google.com In the second subsection the concept of a contraction semigroup is discussed
and it is shown how transient bounds can be estimated via Liapunov norms.
These are auxiliary norms with respect to which a given system is contractive. 

 books.google.com A strongly continuous semigroup T on X is called a strongly continuous
contraction semigroup (or just a contraction semigroup for the sake of brevity) if Tt
⩽ 1holdsforallt ⩾ 0. The introduction of mdissipative operators is motivated by
the ... 

 books.google.com Semigroups with this special property are called contraction semigroups.
Definition 2.2.1 T(t) is a contraction semigroup if it is a Cosemigroup that satisfies
an estimate  T(t) \\ < 1 for all t > 0. m We shall now give necessary and sufficient
... 

 books.google.com Let L = C0 be the space of continuousfunctions φ : S → R, that vanish at infinity.
For φ ∈ C0 define: φ∞ = sup φ(x). x∈S A strongly continuous contraction
positive semigroup on C0 is called a Feller semigroup. Example 2 Let Q be a
measure ... 

 books.google.com endomorphisms on G and all endomorphisms are on G. If a semigroup consists
of ^adjoint (nonnegative) (contraction) endomorphisms we say that it is a ^
adjoint {nonnegative) {contraction) semigroup. If, moreover, all functions Ttg{x)
are ... 

 books.google.com conservative system is lossless if and only if its semigroup is strongly stable
together with its adjoint. ... Combining the two transformations we get an
orthogonal unitary dilation of the original contraction semigroup, which is unique
up to unitary ... 

 books.google.com A strongly continuous semigroup {Q(t)}t>o is said to be a contraction semigroup if
Q(t)l < 1 for £ > 0. See Examples 4.1.3, 4.1.5 and 4.3.4 for some contraction
semigroups, and Exercise 19 of Chapter 1 for analysis of the generator of the ... 

 books.google.com generator of the semigroup is defined by Ah — lim : h s>0+ IS on the set 3t(A) of
vectors h E H for which this limit exists. ... For any strongly continuous semigroup
{T(s)}s>o of contractions on a Hilbert space H there exists a unitary group ... 

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