Young’s lattice, the lattice of all Young diagrams, has the Robinson-Schensted-Knuth correspondence, the correspondence between certain matrices and pairs of semi-standard Young tableaux with the same shape. Fomin introduced generalized Schur operators to generalize the Robinson-Schensted-Knuth correspondence. In this sense, generalized Schur operators are generalizations of semi-standard Young...

In this manuscript, we will study \({\tilde{o}}\)-convergence in (partially) ordered vector spaces and a kind of convergence space V. A V is called semi-order (in short space), if there exist an W operator T from into W. way, say that with respect to \(\{W, T\}\). net \(\{x_\alpha \}\subseteq V\) said be \({\{W,T\}}\)-order convergent \(x\in write \(x_\alpha \xrightarrow {\{W, T\}}x\)), wheneve...

In this paper, we extend the domains of affirmation and negation operators, and more important, of triangular (semi)norms and (semi)conorms from the unit interval to bounded partially ordered sets. The fundamental properties of the original operators are proven to be conserved under this extension. This clearly shows that they are essentially based upon order-theoretic notions. Consequently, a ...

We show the existence of Banach spaces X, Y such that the set of strictly singular operators ᏿(X,Y) (resp., the set of strictly cosingular operators Ꮿ᏿(X,Y)) would be strictly included in F + (X,Y) (resp., F − (X,Y)) for the nonempty class of closed densely defined upper semi-Fredholm operators Φ + (X,Y) (resp., for the nonempty class of closed densely defined lower semi-Fredholm operators Φ − ...

In this article we investigate disjointly non-singular (DNS) operators. Following [9] say that an operator T from a Banach lattice F into space E is DNS, if no restriction of to subspace generated by disjoint sequence strictly singular. We partially answer question showing class operators forms open subset L(F,E) as soon order continuous. Moreover, show in case DNS and only the norm topology mi...

We prove an approximate spectral theorem for non-self-adjoint operators and investigate its applications to second order differential operators in the semi-classical limit. This leads to the construction of a twisted FBI transform. We also investigate the connections between pseudospectra and boundary conditions in the semi-classical limit. AMS subject classification numbers: 81Q20, 47Axx, 34Lxx.

We prove an approximate spectral theorem for non-self-adjoint operators and investigate its applications to second order differential operators in the semi-classical limit. This leads to the construction of a twisted FBI transform. We also investigate the connections between pseudospectra and boundary conditions in the semi-classical limit.