# On Some Results on Linear Orthogonality Spaces

@article{Kanu2014OnSR, title={On Some Results on Linear Orthogonality Spaces}, author={Richmond U. Kanu and K. Rauf}, journal={Asian Journal of Mathematics and Applications}, year={2014}, volume={2014} }

The existence of an inner product provides a means of introducing the notion of orthogonality in normed linear spaces. The most natural definition of orthogonality is: “x⊥y, if and only if the inner product is zero.” This paper introduces different notions of orthogonality in normed linear spaces and shows that they are all equivalent in real Hilbert spaces. Also, some characterizations of linear orthogonality spaces are given.

## 3 Citations

### Some New Types of Orthogonalities in Normed Spaces and Application in Best Approximation

- Mathematics
- 2016

In this paper, two new types of orthogonality from the generalized Carlssion orthogonality have been studied and some properties of orthogonality in Banach spaces are verified and as best implies…

### On Linear Transformation in Linear Orthogonality Spaces

- Mathematics
- 2015

Let (E, ) be linearly orthogonality space, is orthogonally additive and It is proved that, under suitable assumptions on , is sublinear functional. Furthermore, if is orthogonally additive, then is…

### The Othogonality of Martingale in Birkhoff’s sense and others

- MathematicsTikrit Journal of Pure Science
- 2019

Orthogonality is one of an important the concepts in Mathematics , therefor it will be discussed in this paper, the orthogonality of martingale according to Birkhoff ’s, Roberts’s, Singer’s,…

## References

SHOWING 1-10 OF 26 REFERENCES

### On orthogonally exponential and orthogonally additive mappings

- Mathematics
- 1997

Let E be a real inner product space, (F,+) an abelian σ-bounded topological group, and K a discrete subgroup of F . It is proved that (under suitable assumptions on E) the Christensen and Baire…

### Orthogonality and linear functionals in normed linear spaces

- Mathematics
- 1947

The natural definition of orthogonality of elements of an abstract Euclidean space is that x ly if and only if the inner product (x, y) is zero. Two definitions have been given [11](2) which are…

### Two mappings related to semi-inner products and their applications in geometry of normed linear spaces

- Mathematics
- 2000

In this paper we introduce two mappings associated with the lower and upper semi-inner product (·, ·)i and (·, ·)S and with semi-inner products [·, ·] (in the sense of Lumer) which generate the norm…

### Orthogonally additive and orthogonally increasing functions on vector spaces.

- Mathematics
- 1975

A real-valued function /: X—> R on an inner product space X is orthogonally additive if f(x + y) = /(JC) + f(y) whenever x l y . We extend this concept to more general spaces called orthogonality…

### SEMI-INNER-PRODUCT SPACES

- Mathematics
- 1961

function as a particular Banach space (whose norm satisfies the parallelogram law), but rather as an inner-product space. It is in terms of the innerproduct space structure that most of the…

### Inner products in normed linear spaces

- Mathematics
- 1947

Let T be any normed linear space [l, p. S3]. Then an inner product is defined in T if to each pair of elements x and y there is associated a real number (x, y) in such a way that (#, y) » (y, x),…

### Functional Analysis and Semi-Groups

- MathematicsNature
- 1949

THIS work of Prof. Einar Hille is one of the important mathematical books of the century ; it should be read seriously by every mathematician. The subject of semi-groups is one of great and growing…

### Best Approximation in Normed Linear Spaces by Elements of Linear Subspaces

- Mathematics
- 1970

espace lineaire norme # espace metrique # meilleure approximation # sous-espace lineaire # sous-espace lineaire de dimension finie # sous-espace lineaire ferme de codimension finie # element…

### Orthogonality in normed linear spaces

- Mathematics
- 1962

Let B be a real normed l inear space. We will say t ha t B is Eucl idean if the re is a symmet r i c bi l inear funct ional (u, v) (called the inner p roduc t of u and v) defined for u, v e B , such…