 About 559 results  books.google.com Jeffrey Bergen, Susan Montgomery  1994  Preview ... and counitary); c) invertible left Acolinear maps A » A (which is unitary/
counitary/unitary and counitary). All of these sets are nonempty. 3.11 REMARK.
Fix such a unitary and counitary isomorphism A £* A 8 B as in (3. 10. 2. Quotient
Theory ... 

 books.google.com In the applications when we deal with higher genus weight enumerators, it is
convenient to have a name for the hyperbolic counitary group of a matrix ring of
a form ring. Since the matrix ring construction is functorial, the hyperbolic co
unitary ... 

 books.google.com Thus: over R, counitary means unitary. over K, counitary means unitary or anti
unitary. over Q, counitary means something new. It should be emphasized that
complex conjugation a > c<* defines an automorphism in the complex field K but
... 

 books.google.com A graded coassociative, counitary, coaugmented, coalgebra over a field F is a
graded Fmodule, B, together with a coproduct map q : B — B &F B, counit, i.e. a
graded Fmodule morphism 1* : B–R so that (id & 1”) p = (1" & id) p = id, and ... 

 books.google.com al ((<* ) ) , where we have written Ot for the inverse to the automorphism X Y A co
unitary operator U is a mapping of the space V which has an inverse and obeys (
uy)* (u 0  ( / 0)u . It follows that U is colinear. If linear, U is called unitary. 

 books.google.com Definition 2.7 ([Q]) Let C be a DG counitary coalgebra. Suppose that there exists
an element lc of C such that A(lc) = lc ® lc, ec(lc) = 1. We define subspaces FrC, r
> 0 as follows: FoC = k\c; FrC = {xe C  Ac(x) x® lc  lc ®x 6 F^C ® Fr\C} C is ... 

 books.google.com THEOREM 7. The part A^ of operator A, with the domain D(AJ) = H2m(Q,)nHQl(n)
x HTM(£1) is an ininitesimal generator of Co unitary group on the space = i/p^fi) x
L^i^l) and it is given by T(t)(wuw2) = sm{Xnt) Tn = < XI \coa(>^nt)y](wh'Pn ... 

 books.google.com Then U* :: {U*(t) : t G R1} is a semigroup with generator G*. The semigroup U is a
selfadjoint COsemigroup,' that is, U(t) is selfadjointfor all t G R1 if and only if its
generator is selfadjoint. DEFINITION 5.19 A COunitary group is a COgroup of ... 

 books.google.com Definition 5.19 A Counitary group is a Cogroup of unitary operators. We can
now introduce Theorem 5.20 (Stone's Theorem) Let H be a Hilbert space. An
operator G : H 3 D(G) —fHis the generator of a Counitary group U on H if and
only if G ... 

 books.google.com These maps satisfy the following properties: Coassociativity: The diagram H → H
& H al As, H & H — H & H & H 1 & A commutes: this is the "dual” diagram to that
for associativity of the multiplication map pl; Counitary: the diagrams H — H & H ... 

 