Mixing
Does there exist a connection between contractive completely positive map and surjective map
Clash Royale CLAN TAG#URR8PPP
up vote
0
down vote
favorite
If $psi:A rightarrow M_n(mathbbC)$ is a c.c.p map.What is the relationship between c.c.p maps and surjective maps?Can we deduce that $psi$ is a surjective map?If not,does there a close connection between a c.c.p map and a homomorphism?
operator-theory operator-algebras c-star-algebras
asked Jul 31 at 16:29
mathrookie
428211
add a comment |Â
up vote
0
down vote
favorite
If $psi:A rightarrow M_n(mathbbC)$ is a c.c.p map.What is the relationship between c.c.p maps and surjective maps?Can we deduce that $psi$ is a surjective map?If not,does there a close connection between a c.c.p map and a homomorphism?
operator-theory operator-algebras c-star-algebras
asked Jul 31 at 16:29
mathrookie
428211
No, as mentioned below. However, there is a useful correspondence between ccp maps into $M_n(mathbbC)$ and certain linear functionals on $M_n(A)$. Have a look at Chapter 6 of Vern Paulsen's book "Completely bounded maps and operator algebras".
– Prahlad Vaidyanathan
Aug 1 at 2:29
add a comment |Â
up vote
0
down vote
favorite
up vote
0
down vote
favorite
If $psi:A rightarrow M_n(mathbbC)$ is a c.c.p map.What is the relationship between c.c.p maps and surjective maps?Can we deduce that $psi$ is a surjective map?If not,does there a close connection between a c.c.p map and a homomorphism?
operator-theory operator-algebras c-star-algebras
asked Jul 31 at 16:29
mathrookie
428211
If $psi:A rightarrow M_n(mathbbC)$ is a c.c.p map.What is the relationship between c.c.p maps and surjective maps?Can we deduce that $psi$ is a surjective map?If not,does there a close connection between a c.c.p map and a homomorphism?
operator-theory operator-algebras c-star-algebras
asked Jul 31 at 16:29
mathrookie
428211
asked Jul 31 at 16:29
mathrookie
428211
asked Jul 31 at 16:29
mathrookie
428211
asked Jul 31 at 16:29
mathrookie
428211
428211
No, as mentioned below. However, there is a useful correspondence between ccp maps into $M_n(mathbbC)$ and certain linear functionals on $M_n(A)$. Have a look at Chapter 6 of Vern Paulsen's book "Completely bounded maps and operator algebras".
– Prahlad Vaidyanathan
Aug 1 at 2:29
add a comment |Â
No, as mentioned below. However, there is a useful correspondence between ccp maps into $M_n(mathbbC)$ and certain linear functionals on $M_n(A)$. Have a look at Chapter 6 of Vern Paulsen's book "Completely bounded maps and operator algebras".
– Prahlad Vaidyanathan
Aug 1 at 2:29
No, as mentioned below. However, there is a useful correspondence between ccp maps into $M_n(mathbbC)$ and certain linear functionals on $M_n(A)$. Have a look at Chapter 6 of Vern Paulsen's book "Completely bounded maps and operator algebras".
– Prahlad Vaidyanathan
Aug 1 at 2:29
No, as mentioned below. However, there is a useful correspondence between ccp maps into $M_n(mathbbC)$ and certain linear functionals on $M_n(A)$. Have a look at Chapter 6 of Vern Paulsen's book "Completely bounded maps and operator algebras".
– Prahlad Vaidyanathan
Aug 1 at 2:29
add a comment |Â
1 Answer
1
active
oldest
votes
up vote
0
down vote
No, not at all. Take any state $f$ on $A$, and then $alongmapsto f(a),I$ is ucp and it is as far from surjective as it can be (well, more properly, the zero map is also ccp; my example is unital, at least).
As for $*$-homomorphisms, they are all ccp (easy exercise, that should definitely be done if it is not obvious to you).
answered Jul 31 at 23:34
Martin Argerami
115k1071164
add a comment |Â
1 Answer
1
active
oldest
votes
1 Answer
1
active
oldest
votes
active
oldest
votes
active
oldest
votes
up vote
0
down vote
No, not at all. Take any state $f$ on $A$, and then $alongmapsto f(a),I$ is ucp and it is as far from surjective as it can be (well, more properly, the zero map is also ccp; my example is unital, at least).
As for $*$-homomorphisms, they are all ccp (easy exercise, that should definitely be done if it is not obvious to you).
answered Jul 31 at 23:34
Martin Argerami
115k1071164
add a comment |Â
up vote
0
down vote
No, not at all. Take any state $f$ on $A$, and then $alongmapsto f(a),I$ is ucp and it is as far from surjective as it can be (well, more properly, the zero map is also ccp; my example is unital, at least).
As for $*$-homomorphisms, they are all ccp (easy exercise, that should definitely be done if it is not obvious to you).
answered Jul 31 at 23:34
Martin Argerami
115k1071164
add a comment |Â
up vote
0
down vote
up vote
0
down vote
No, not at all. Take any state $f$ on $A$, and then $alongmapsto f(a),I$ is ucp and it is as far from surjective as it can be (well, more properly, the zero map is also ccp; my example is unital, at least).
As for $*$-homomorphisms, they are all ccp (easy exercise, that should definitely be done if it is not obvious to you).
answered Jul 31 at 23:34
Martin Argerami
115k1071164
No, not at all. Take any state $f$ on $A$, and then $alongmapsto f(a),I$ is ucp and it is as far from surjective as it can be (well, more properly, the zero map is also ccp; my example is unital, at least).
As for $*$-homomorphisms, they are all ccp (easy exercise, that should definitely be done if it is not obvious to you).
answered Jul 31 at 23:34
Martin Argerami
115k1071164
answered Jul 31 at 23:34
Martin Argerami
115k1071164
answered Jul 31 at 23:34
Martin Argerami
115k1071164
answered Jul 31 at 23:34
Martin Argerami
115k1071164
115k1071164
add a comment |Â
add a comment |Â
Sign up or log in
StackExchange.ready(function ()
StackExchange.helpers.onClickDraftSave('#login-link');
);
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
StackExchange.ready(
function ()
StackExchange.openid.initPostLogin('.new-post-login', 'https%3a%2f%2fmath.stackexchange.com%2fquestions%2f2868227%2fdoes-there-exist-a-connection-between-contractive-completely-positive-map-and-su%23new-answer', 'question_page');
);
Post as a guest
Sign up or log in
StackExchange.ready(function ()
StackExchange.helpers.onClickDraftSave('#login-link');
);
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Sign up or log in
StackExchange.ready(function ()
StackExchange.helpers.onClickDraftSave('#login-link');
);
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Sign up or log in
StackExchange.ready(function ()
StackExchange.helpers.onClickDraftSave('#login-link');
);
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
No, as mentioned below. However, there is a useful correspondence between ccp maps into $M_n(mathbbC)$ and certain linear functionals on $M_n(A)$. Have a look at Chapter 6 of Vern Paulsen's book "Completely bounded maps and operator algebras".
– Prahlad Vaidyanathan
Aug 1 at 2:29