A partial isometries and generalized inverses

Laura Arias

Description

A-partial isometries and generalized inverses M. Laura Arias Instituto Argentino de Matemática- CONICET Argentina Operator theory and related topics Lille 2010 M. Laura Arias A-partial isometries and generalized inverses

• hilbertian spaces


• instituto argentino de matemática- conicet argentina


• hilbert space induced


• ?? ?? ?


• semi-norm induced

Informations

• Publié par: profil-urra-2012
• Nombre de lectures: 36
• Langue: English

Extrait

A-partial isometries and generalized inverses

M. Laura Arias

Instituto Argentino de Matemática- CONICET Argentina

Operator theory and related topics Lille 2010

M. Laura Arias

A-partial isometries and generalized inverses

Contents

Definition and basic facts about semi-Hilbertian spaces.

M. Laura Arias

A-partial isometries and generalized inverses

Contents

Definition and basic facts about semi-Hilbertian spaces. Classes of operators on semi-Hilbertian spaces (A-partial isometries).

M. Laura Arias

A-partial isometries and generalized inverses

Contents

Definition and basic facts about semi-Hilbertian spaces.

Classes of operators on semi-Hilbertian spaces (A-partial isometries). Relationship with similar classes of operators on the Hilbert space induced by a positive operator.

M. Laura Arias

A-partial isometries and generalized inverses

Semi-Hilbertian spaces

LetHbe a Hilbert space with inner producth,i.GivenA∈L(H) + , leth,i A the semi-inner product defined by

hξ, ηi A :=hAξ, ηi,for everyξ, η∈ H.

M. Laura Arias

A-partial isometries and generalized inverses

Semi-Hilbertian spaces

LetHbe a Hilbert space with inner producth,i.GivenA∈L(H) + , leth,i A the semi-inner product defined by

hξ, ηi A :=hAξ, ηi,for everyξ, η∈ H.

Byk k A we denote the semi-norm induced byh,i A , i.e.,

kξk A :=hξ, ξi A 1/2 =kA 1/2 ξk ∀ξ∈ H.

M. Laura Arias

A-partial isometries and generalized inverses

Semi-Hilbertian spaces

LetHbe a Hilbert space with inner producth,i.GivenA∈L(H) + , leth,i A the semi-inner product defined by

hξ, ηi A :=hAξ, ηi,for everyξ, η∈ H.

Byk k A we denote the semi-norm induced byh,i A , i.e.,

kξk A :=hξ, ξi A 1/2 =kA 1/2 ξk ∀ξ∈ H.

(H,h,i A )is a semi-Hilbertian space.

M. Laura Arias

A-partial isometries and generalized inverses

Semi-Hilbertian spaces

LetHbe a Hilbert space with inner producth,i.GivenA∈L(H) + , leth,i A the semi-inner product defined by

hξ, ηi A :=hAξ, ηi,for everyξ, η∈ H.

Byk k A we denote the semi-norm induced byh,i A , i.e.,

kξk A :=hξ, ξi A 1/2 =kA 1/2 ξk ∀ξ∈ H.

(H,h,i A )is a semi-Hilbertian space.

Our main goal is to study classes of operators on(H,h,i A ).

M. Laura Arias

A-partial isometries and generalized inverses