4 papers
Maximal right ideals of the Banach algebra of bounded operators on a Banach space
Tomasz Kania, Niels Jakob Laustsen
We study finitely generated maximal right ideals of the Banach algebra of bounded operators on a complex Banach space . Every maximal right ideal is either fixe…
Banach's Isometric Conjecture over the Complex Field
Antonio Acuaviva, Tomasz Kania
We complete Banach's isometric conjecture over the complex field. More precisely, if \(X\) is a complex normed space and, for some \(2\leqslant n<\dim_{\C}X\), all its \(n\)-dimens…
Pure infiniteness and primary factorisation
Antonio Acuaviva, Bence Horváth, Tomasz Kania
We show that there is no real or complex indecomposable Banach space with the primary factorisation property (PFP). We relate the PFP of a Banach space to ring-theoretic infini…
Primariness and the Primary Factorisation Property
Antonio Acuaviva, Tomasz Kania
We study the relation between primariness of Banach spaces and the stronger operator-theoretic notions of the primary factorisation property (PFP) and the uniform primary factorisa…