 About 112,000 results  books.google.com Let A : D(A)→X be a densely defined dissipative operator. Then A is m
dissipative if and only if A is closed and A∗ is dissipative. Proof. Suppose that A
is mdissipative. According to Proposition 3.1.9, A is closed and according to
Proposition ... 

 books.google.com H. Isolated Singularities of the Resolvent Let T be a densely defined closed linear
operator in a complex Banach space X and '10 an .... If X is a Hilbert space, then
conversely a maximal dissipative operator with dense domain is mdissipative. 

 books.google.com Consequently, there exists a unique closed operator K in C,(H) such that G(A) = (
A — K). " for any X > 0. K is called the infinitesimal generator of (P). It is clearly m
dissipative” in C,(H) since, OK)'''.< f, A0 recoil). It is an interesting problem ... 

 books.google.com Perturbation results for mdissipative operators In many cases the operator under
consideration can be viewed as a perturbation of an mdissipative operator.
Therefore it is important to know whether the sum of an mdissipative operator
and ... 

 books.google.com We say that A is accretive if — A is dissipative. We shall compare this definition
with Definition 1 (the case where X is a Hilbert space). Definition 6. mdissipative;
mstrongly dissipative; maccretive operators We say that an operator A with ... 

 books.google.com 2.2. Definition. and. main. properties. of. mdissipative. operators. Definition 2.2.1.
An operator A in X is dissipative if uAj4u > H, for all u e D(A) and all A > 0.
Definition 2.2.2. An operator A in X is mdissipative if (i) A is dissipative; (ii) for all
A ... 

 books.google.com In particular, a maximal dissipative operator on the whole space X is called
simply a maximal dissipative operator. (ii) A dissipative operator A with R(I~XA) =
X (2.19) for all X > 0 is called an mdissipative operator. Lemma 2.12. (i) Let Sx c
S2 ... 

 books.google.com A linear operator is dissipative if and only if, for all u S D(A), and A > 0 we have (
A/A)uU>uU. (2.6.11) This shows that a dissipative operator has a closed range
. Dissipative operators satisfying R(I  A) = X (2.6.12) are called mdissipative. 

 books.google.com Recall that the operator T in the Hilbert space H is called dissipative if Im (Tf,f) ≥
0 for all f ∈ Dom(T). A dissipative operator T is called maximal dissipative (m
dissipative) if one of the equivalent conditions is satisfied: • T has no dissipative ... 

 books.google.com Any dissipative operator is closable. The dissipative operator ^f is called m
dissipative if the range of A — ,e/ coincides with JV for some (and consequently
for any) A > 0. An operator stf with dense domain is mdissipative if and only if it is
the ... 

 