Operators which have a closed quasi-nilpotent part

QUASI - SIMILAR MODELS FOR NILPOTENT OPERATORS ( x )

Every nilpotent operator on a complex Hilbert space is shown to be quasi-similar to a canonical Jordan model. Further, the para-reflexive operators are characterized generalizing a result of Deddens and Fillmore. A familiar result states that each nilpotent operator on a finite dimensional complex Hubert space is similar to its adjoint. One proof proceeds by showing that both a nilpotent operat...

Which Chessboards have a Closed Knight's Tour within the Cube?

A closed knight’s tour of a chessboard uses legal moves of the knight to visit every square exactly once and return to its starting position. When the chessboard is translated into graph theoretic terms the question is transformed into the existence of a Hamiltonian cycle. There are two common tours to consider on the cube. One is to tour the six exterior n × n boards that form the cube. The ot...

Closed Sets Which Consistently Have Few Translates Covering the Line

We characterize the compact subsets K of 2ω for which one can force the existence of a set X of cardinality less than the continuum such that K +X = 2ω .

Equivalence operators in nilpotent systems

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...