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On orthogonally additive injections and surjections

100%

Baron K.

Commentationes Mathematicae

2015

tom 55

nr 2

Let \(E\) be a real inner product space of dimension at least 2 and \(V\) a linear topological Hausdorff space. If \(\operatorname{card}E\leq \operatorname{card} V\), then the set of all orthogonally additive injections mapping \(E\) into \(V\) is dense in the space of all orthogonally additive functions from \(E\) into \(V\) with the Tychonoff topology. If \(\operatorname{card}V\leq \operatorname{card}E\), then the set of all orthogonally additive surjections mapping \(E\) into \(V\) is dense in the space of all orthogonally additive functions from \(E\) into \(V\) with the Tychonoff topology.

On The Continuous Dependence Of Solutions To Orthogonal Additivity Problem On Given Functions

86%

Baron K.

Annales Mathematicae Silesianae

2015

tom 29

nr 1

19-23

We show that the solution to the orthogonal additivity problem in real inner product spaces depends continuously on the given function and provide an application of this fact.

On Orthogonally Additive Functions With Big Graphs

86%

Baron K.

Annales Mathematicae Silesianae

2017

tom 31

nr 1

57-62

Let E be a separable real inner product space of dimension at least 2 and V be a metrizable and separable linear topological space. We show that the set of all orthogonally additive functions mapping E into V and having big graphs is dense in the space of all orthogonally additive functions from E into V with the Tychonoff topology.

Ograniczanie wyników

2 Annales Mathematicae Silesianae

1 Commentationes Mathematicae

3 Baron K.

1 2017

2 2015

Wyniki wyszukiwania

On orthogonally additive injections and surjections

On The Continuous Dependence Of Solutions To Orthogonal Additivity Problem On Given Functions

On Orthogonally Additive Functions With Big Graphs