Image for the paper "The height of an infinite parallelotope is infinite"
Image for the paper "The height of an infinite parallelotope is infinite"
Image for the paper "The height of an infinite parallelotope is infinite"
Image for the paper "The height of an infinite parallelotope is infinite"
Image for the paper "The height of an infinite parallelotope is infinite"
Image for the paper "The height of an infinite parallelotope is infinite"
Image for the paper "The height of an infinite parallelotope is infinite"
Image for the paper "The height of an infinite parallelotope is infinite"
Image for the paper "The height of an infinite parallelotope is infinite"
Image for the paper "The height of an infinite parallelotope is infinite"
Image for the paper "The height of an infinite parallelotope is infinite"
Image for the paper "The height of an infinite parallelotope is infinite"
Image for the paper "The height of an infinite parallelotope is infinite"
Image for the paper "The height of an infinite parallelotope is infinite"
Image for the paper "The height of an infinite parallelotope is infinite"
Image for the paper "The height of an infinite parallelotope is infinite"

Infinitely high parallelotopes

Linear algebra

We demonstrate that the height of an infinite parallelotope is infinite if no non-trivial combinations of its edges belong to $l_2(\mathbb N)$.

The height of an infinite parallelotope is infinite

Submitted

A. V. Kosyak

We show that Γ(f0,f1,…,fm)Γ(f1,…,fm)=∞ for m+1 vectors having the properties that no non-trivial linear combination of them belongs to l2(ℕ). This property is essential in the proof of the irreducibility of unitary representations of some infinite-dimensional groups.

Submitted

A. V. Kosyak