A C*-ALGEBRA APPROACH TO THE IRREDUCIBILITY OF COWEN-DOUGLAS OPERATORS

LetHbeaseparableindnitedimensionalHilbertspaceoverthefieldCandletL(H)(resp.K(H))denotethealgebraofallboundedlinearoperators(resp.allcompactoperators)onH.ForTEL(H),wedenotebyR(T)(resp.KerT)therange(resp.thenullspace)ofT.Accordingto[2],Bit(fl)consistsofallCowen-DouglasoperatorsTEL(H)satisfyingfollowingconditions:(l)fiCa(T)isaconectedopensubsetinC;(2)R(w--T)=HanddimKer(w--T)=n相似文献   

f3组态离子在四角场中的基矢矩阵元

通过选用与群链[(O⊃D₄⊃C₄)×SU(2)]相匹配的单电子基矢,使其直积构成多电子fN体系的O⊃D₄⊃C₄旋量群的不可约表示的基矢,并讨论了有关的Coulomb矩阵元、Casimir矩阵元、旋-轨偶合矩阵元和晶体场作用矩阵元.     

关于既约非负矩阵优势比的界

本文改进了Ａ．Ｍ．Ｏｓｔｒｏｗｓｋｉ和佟文廷的结果,得到了关于既约非负矩阵优势比的新界．     

vspace{-1cm}$W(2,\boldsymbol{n})$和$H(2,\boldsymbol{n})$的$p$-特征标高度为$2$的不可约模的分类$^{}$

研究$p$-\!\!特征标高度等于$2$的$W(2,\boldsymbol{n})$和$H(2,\boldsymbol{n})$ 的不可约表示, 给出了当 $p$-\!\!特征标$\chi $的 高度等于$2$时, $L=X(2,\boldsymbol{n})$, $X=W,H$ 的不可约$L$-\!\!模 同构类代表元集合.     

Apollonius circles and irreducibility criteria for polynomials

We prove the irreducibility of integer polynomials $f\left(X\right)$ whose roots lie inside an Apollonius circle associated to two points on the real axis with integer abscissae $a$ and $b$, with ratio of the distances to these points depending on the canonical decomposition of $f\left(a\right)$ and $f\left(b\right)$. In particular, we obtain irreducibility criteria for the case where $f\left(a\right)$ and $f\left(b\right)$ have few prime factors, and $f$ is either an Eneström–Kakeya polynomial, or has a large leading coefficient. Analogous results are also provided for multivariate polynomials over arbitrary fields, in a non-Archimedean setting.     

Convex bodies and asymptotic invariants for powers of monomial ideals

Continuing a well established tradition of associating convex bodies to monomial ideals, we initiate a program to construct asymptotic Newton polyhedra from decompositions of monomial ideals. This is achieved by forming a graded family of ideals based on a given decomposition. We term these graded families powers since they generalize the notions of ordinary and symbolic powers. Asymptotic invariants for these graded families are expressed as solutions to linear optimization problems on the respective convex bodies. This allows to establish a lower bound on the Waldschmidt constant of a monomial ideal by means of a more easily computable invariant, which we introduce under the name of naive Waldschmidt constant.