Ultraprimeness of the Lorentz algebra

Strašek, Rok

doi:10.1007/s00229-005-0601-2

Cited by 1 publication

(1 citation statement)

References 6 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Let us say that an operator algebra A ⊂ B(H) has the conjugation with lower bound property (CLBP) if there exits a constant 0 < δ ≤ 1 such that a → XaX −1 cb ≥ δ X X −1 for every invertible X ∈ B(H). This notion resembles that of ultraprimeness for general Banach algebras introduced in [18], which has attracted some interest in past years (see [5], [26] and [28] for instance). The difference here is that we do not assume that the element X lies in the algebra A, and we restrict our attention to conjugation operators rather than general multiplication operators M X,Y (a) = XaY .…”

Section: Possible Extensions Of Our Resultsmentioning

confidence: 99%

Completely bounded isomorphisms of operator algebras and similarity to complete isometries

Clouâtre¹

2015

Indiana Univ. Math. J.

View full text Add to dashboard Cite

A well-known theorem of Paulsen says that if A is a unital operator algebra and ϕ : A → B(H) is a unital completely bounded homomorphism, then ϕ is similar to a completely contractive map ϕ ′ . Motivated by classification problems for Hilbert space contractions, we are interested in making the inverse ϕ ′−1 completely contractive as well whenever the map ϕ has a completely bounded inverse. We show that there exist invertible operators X and Y such that the map XaX −1 → Y ϕ(a)Y −1 is completely contractive and is "almost" isometric on any given finite set of elements from A with non-zero spectrum. Although the map cannot be taken to be completely isometric in general, we show that this can be achieved if A is completely boundedly isomorphic to either a C * -algebra or a uniform algebra. In the case of quotient algebras of H ∞ , we translate these conditions in function theoretic terms and relate them to the classical Carleson condition.2010 Mathematics Subject Classification. Primary:47L30, 46L07, 47L55.

show abstract

Section: Possible Extensions Of Our Resultsmentioning

confidence: 99%

Completely bounded isomorphisms of operator algebras and similarity to complete isometries

Clouâtre¹

2015

Indiana Univ. Math. J.

View full text Add to dashboard Cite

show abstract

Ultraprimeness of the Lorentz algebra

Cited by 1 publication

References 6 publications

Completely bounded isomorphisms of operator algebras and similarity to complete isometries

Completely bounded isomorphisms of operator algebras and similarity to complete isometries

Contact Info

Product

Resources

About