The conjugates and preconjugates of linear operators
The conjugates and preconjugates of linear operators
 Download this document for free, or read online. Document in PDF available to download.
The preconjugate  Examples of admissible  Applications  Acknowledgements
Tipo de documento: Artículo  Article
Source: http://www.bdigital.unal.edu.co
Teaser
MATEMATICAS
THE
CONJUGATES
PURAS
AND PRECONJUGATES
OF LINEAR
OPERATORS
by
KATHY
an d S.
Gol dberg,
studying
study
T
when
one
can gain know Iedge
Lebesgue
operates
remarks
space
spaces
represent
between
a linear
and
operator
otherwi se noted
x, y, x
their
and .8(T)
and
v
difficult
to
(2 .
) is rather
y
dualspaces,
X and
Roo
Y.
and
For example,
e
is a map between
to operators
X and
Y
T by
1
on:t:,,
the
al mo st everywhere.
discussion
X
to
applicable
of fun ction s bounded
and
eoo,since
2
operator
it is at times
spaces,
from
by A.
E.
Taylor
a I inear
is a map between
are also
In the following
linear
tQ)into
study
about
THcwever,
of an operator
These
~1
operator
While the conjugate
the preconjugate
and
PRE CON JUG ATE
T isamapfrom
the preconjugate
E.
U.
A.
With the aid of a systematic
its conjugate
complicated.
X,
THE
De fin i t i o n .
1.
FORBES
cle Marylancl.
( Universiclacl
1.
K.
Y
will
dualor
always
adjoint
spcce s.i T will
will be the domain
will
be elements
of
be normed
of
T.
X, Y, X
Unless
and
Y
respectively.
Definition.
for all
x ~
Let
In
X.
words
Let
implies
=
be its
{y6Y
continuous
like to define
=
x
A be a linear
T
ff(T)
the unique
F
A subset
operator
v
extension
the preconjugate,
in
X if xx
=
0
O.
conjugate

F of X is total
A
mapping
operator
X to Y with.tY(A)
mapping
is continuous
Y to X.
on d(A)},
of
v
T,
of T mapping
A to the whole
of
X to
and
dense
In other
Tyis
X.
We would
Y.T
should
3
be equal
v
to
A
or at least
A x : A y x
xfi:f}(T)
= Tyx
if there
and we define
for all
exists
YEY
T x = y.
that the domain
a linear
the
preconjugate,
An element
vv
that
Then
x
T,
of
X lies
E
we say
for all
defined
y~.b(T),
we require
linear
with ff(T)
X to
total
spaces
and
Y,
Then
in
Y and is defined
of T
if there
as follows.
exi st...