We use the definition of probabilistic normed space (briefly, PN space) proposed by Alsina, Schweizer and Sklar and investigate the properties of different spaces of linear operators between PN spaces. Because PN spaces are not necessarily topological linear spaces, the set of bounded linear operators and the set of continuous and bounded linear operators are not necessarily linear subspaces of $L$ (the vector space of linear operators from a PN space $V_1$ to a PN space $V_2$ ). Some necessary conditions are indicated. The probabilistic radius of sets is used to study the norms of linear operators (from $V_1$ to $V_2$). Then characterizations of classes of linear operators are shown. Finally, the several properties of families of linear operators are discussed.
Probabilistic Norms for Linear Operators
SEMPI, Carlo
1998-01-01
Abstract
We use the definition of probabilistic normed space (briefly, PN space) proposed by Alsina, Schweizer and Sklar and investigate the properties of different spaces of linear operators between PN spaces. Because PN spaces are not necessarily topological linear spaces, the set of bounded linear operators and the set of continuous and bounded linear operators are not necessarily linear subspaces of $L$ (the vector space of linear operators from a PN space $V_1$ to a PN space $V_2$ ). Some necessary conditions are indicated. The probabilistic radius of sets is used to study the norms of linear operators (from $V_1$ to $V_2$). Then characterizations of classes of linear operators are shown. Finally, the several properties of families of linear operators are discussed.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
