## A Weak Extension of Complex Structure on Hilbert Spaces

**Authors:** Naum E. Salis

The purpose of this paper is to try to replicate what happens in C on spaces where there are more then one of immaginary units. All these spaces, in our definition, will have the same Hilbert structure. At first we will introduce the sum and product operations on C(H):=RxH (where H is an Hilbert space), then we'll investigate on its algebraic properties. In our construction we lose only the associative of multiplication regardless of H, exept when dim H=1 (in this case RxH = C), and this is why we say "weak extension". One of the most important result of this study is the Weak Integrity Theorem according to which in particular conditions there exist zero divisors. The next result is the Foundamental Theorem according to which for all z in C(H) there exists w in C(H) such that z=w^2. Afterwards we will study tranformations between these spaces which keep operation (that's why we will call them C-morphisms). At the end we will look at the "commutative" functions, i.e. maps C(H) to C(H') which can be rapresented by complex transformations C to C

**Comments:** 15 Pages.

**Download:** **PDF**

### Submission history

[v1] 2019-07-25 04:57:09

**Unique-IP document downloads:** 17 times

Vixra.org is a pre-print repository rather than a journal. Articles hosted may not yet have been verified by peer-review and should be treated as preliminary.
In particular, anything that appears to include financial or legal advice or proposed medical treatments should be treated with due caution.
Vixra.org will not be responsible for any consequences of actions that result from any form of use of any documents on this website.

**Add your own feedback and questions here:**

*You are equally welcome to be positive or negative about any paper but please be polite. If you are being critical you must mention at least one specific error, otherwise your comment will be deleted as unhelpful.*

*
*