Strictly positive linear functional: If there is one, there are ...
Jun 28, 2024 · 1 After a slight reframing, the question is really asking about the following: If F ⊂ Lp is a proper closed subspace of Lp, does there exists two (and therefore uncountably many) different …
linear algebra - What is the correct definition for positive operator ...
Jul 15, 2016 · Both definitions are correct and common in certain contexts. Yours is common for the context of finite dimensional vector spaces (in which one may use "positive semidefinite" for your …
Extending a positive linear functional in finite dimensions
I have my own proof, but it is complicated and uses the Bauer-Namioka condition for extension of positive linear functionals on ordered vector spaces of any dimension. Question: What is this simple …
Is a positive linear functional on $L^p$ necessarily bounded?
By the Hahn-Banach version for positive linear functionals, $\Lambda$ can be extended to the entire space to a positive linear functional, which is not going to be bounded.$\endgroup$ uniquesolution – …
Is greatest common divisor of two numbers really their smallest linear ...
In a lecture note from MIT on number theory says: Theorem 5. The greatest common divisor of a and b is equal to the smallest positive linear combination of a and b. For example, the greatest ...
Positive Linear Functional on - Mathematics Stack Exchange
Positive Linear Functional on C[0, 1] C [0, 1] Ask Question Asked 11 years, 3 months ago Modified 11 years, 3 months ago
Linear functionals can be decomposed as linear combinations of …
Every hermitian linear functional is a combination of two positive ones. Even in the case of commutative C^* algebras this is non-trivial, it is the Hahn-Jordan decomposition of a finite real-valued measure.
Why is every positive linear map between $C^*$-algebras bounded?
Jun 22, 2013 · We know that every positive linear functional on a C∗ C ∗ -algebra is bounded. How can we prove every positive linear map between C∗ C ∗ -algebras is bounded?
Why are positive linear functionals on - Mathematics Stack Exchange
Jan 23, 2022 · Why are positive linear functionals on C∗ C ∗ -algebras always bounded? Ask Question Asked 12 years, 11 months ago Modified 4 years ago
On the proof that positive linear functionals are continuous
Nov 25, 2021 · On the proof that positive linear functionals are continuous Ask Question Asked 4 years, 2 months ago Modified 4 years, 2 months ago