Contractible Köthe co-echelon algebras

Piszczek, Krzysztof

doi:10.2989/16073606.2019.1579765

Cited by 6 publications

(17 citation statements)

References 14 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Recall that ( , ) denotes the space of all linear and continuous module maps and ( ) ∶= • ( ∈ ℕ). In [20] the same concept was defined only for short sequences therefore we now show equivalence of these two definitions.…”

Section: Projective and Flat Modulesmentioning

confidence: 64%

“…Recall that

_{A} L false(P, X false)

denotes the space of all linear and continuous module maps and

D_{n} false(f false) : = d_{n} \circ f false(n \in double-struckN false)

. In the same concept was defined only for short sequences therefore we now show equivalence of these two definitions. Proposition Let A be a DF‐algebra and let P be a left DF‐ A ‐module.…”

Section: Projective and Flat Modulesmentioning

confidence: 91%

“…Proof

(i i i) \Leftrightarrow (i i)

follows from [, Theorem 11] and

(i i) \Rightarrow (i)

follows from Remark . It remains to prove that “amenable” implies “unital”.…”

Section: Amenability Of Kp(v)mentioning

confidence: 92%

“…Let 1 ⩽ < ∞ and let ( ) be a Köthe co-echelon algebra. TFAE: [20,Theorem 11] and ( ) ⇒ ( ) follows from Remark 4.1. It remains to prove that "amenable" implies "unital".…”

Section: Amenabilit Y Of ( )mentioning

confidence: 96%

“…A comprehensive study of these spaces may be found in . Köthe co‐echelon algebras appear as a main object of investigation in and .…”

Section: Preliminariesmentioning

confidence: 99%

See 4 more Smart Citations

Amenable Köthe co‐echelon algebras

Piszczek

2019

Mathematische Nachrichten

Self Cite

View full text Add to dashboard Cite

show abstract

Section: Projective and Flat Modulesmentioning

confidence: 64%

“…Recall that

_{A} L false(P, X false)

denotes the space of all linear and continuous module maps and

D_{n} false(f false) : = d_{n} \circ f false(n \in double-struckN false)

. In the same concept was defined only for short sequences therefore we now show equivalence of these two definitions. Proposition Let A be a DF‐algebra and let P be a left DF‐ A ‐module.…”

Section: Projective and Flat Modulesmentioning

confidence: 91%

“…Proof

(i i i) \Leftrightarrow (i i)

follows from [, Theorem 11] and

(i i) \Rightarrow (i)

follows from Remark . It remains to prove that “amenable” implies “unital”.…”

Section: Amenability Of Kp(v)mentioning

confidence: 92%

“…Let 1 ⩽ < ∞ and let ( ) be a Köthe co-echelon algebra. TFAE: [20,Theorem 11] and ( ) ⇒ ( ) follows from Remark 4.1. It remains to prove that "amenable" implies "unital".…”

Section: Amenabilit Y Of ( )mentioning

confidence: 96%

“…A comprehensive study of these spaces may be found in . Köthe co‐echelon algebras appear as a main object of investigation in and .…”

Section: Preliminariesmentioning

confidence: 99%

See 3 more Smart Citations

Amenable Köthe co‐echelon algebras

Piszczek

2019

Mathematische Nachrichten

Self Cite

View full text Add to dashboard Cite

show abstract

General approach to Köthe echelon algebras

Ciaś

Piszczek

2021

Mathematische Nachrichten

Self Cite

View full text Add to dashboard Cite

We provide a study of Köthe sequence algebras. These are Fréchet sequence algebras which can be viewed as abstract analogoues of algebras of smooth or holomorphic functions. Of particular treatment are the following properties: unitality,-convexity,-property and variants of amenability. These properties are then checked against the topological (DN)-(Ω) type conditions of Vogt-Zaharjuta. Description of characters and closed ideals in Köthe echelon algebras is provided. We show that these algebras are functionally continuous and we characterize completely which of them factor. Moreover, we prove that closed subalgebras of Montel-convex Köthe echelon algebras are Köthe echelon algebras as well and we give a version of Stone-Weiestrass theorem for these algebras. We also emphasize connections with the algebra of smooth operators.

show abstract