Triangular truncation and normal limits of nilpotent operators

some properties of fuzzy hilbert spaces and norm of operators

in this thesis, at first we investigate the bounded inverse theorem on fuzzy normed linear spaces and study the set of all compact operators on these spaces. then we introduce the notions of fuzzy boundedness and investigate a new norm operators and the relationship between continuity and boundedness. and, we show that the space of all fuzzy bounded operators is complete. finally, we define...

Products of commuting nilpotent operators

Matrices that are products of two (or more) commuting square-zero matrices and matrices that are products of two commuting nilpotent matrices are characterized. Also given are characterizations of operators on an infinite dimensional Hilbert space that are products of two (or more) commuting square-zero operators, as well as operators on an infinite-dimensional vector space that are products of...

Equivalence operators in nilpotent systems

Invariants of the nilpotent and solvable triangular Lie algebras

Invariants of the coadjoint representation of two classes of Lie algebras are calculated. The first class consists of the nilpotent Lie algebras T (M), isomorphic to the algebras of upper triangular M × M matrices. The Lie algebra T (M) is shown to have [M/2] functionally independent invariants. They can all be chosen to be polynomials and they are presented explicitly. The second class consist...

Nilpotent groups with three conjugacy classes of non-normal subgroups

‎Let $G$ be a finite group and $nu(G)$ denote the number of conjugacy classes of non-normal subgroups of $G$‎. ‎In this paper‎, ‎all nilpotent groups $G$ with $nu(G)=3$ are classified‎.