A Banach space operator T ∈ B(χ) is polaroid if points λ ∈ iso σ(T) are poles of the resolvent of T. Let sa(T), sw(T), saw(T), sSF+(T) and sSF-(T)sigma_a(T), sigma_w(T), sigma_{aw}(T), sigma_{SF_+}(T), rm{and},sigma_{SF_-}(T) denote, respectively, the approximate point, the Weyl, the Weyl essential approximate, the upper semi–Fredholm and lower semi–Fredholm spectrum of T. For A, B and C ∈ B(χ), let M C denote the operator matrix $left( {{ll} A & C 0 & B } right)$left( {begin{array}{ll} A & C 0 & B end{array} } right). If A is polaroid on p0(MC) = {l Î iso s(MC) : 0 < dim (MC - l)-1(0) < ¥}pi_{0}(M_{C}) = {{lambda in {rm iso}, sigma(M_{C}) : 0 < {rm dim} (M_{C} - lambda)^{-1}(0) < infty}}, M 0 satisfies Weyl’s theorem, and A and B satisfy either of the hypotheses (i) A has SVEP at points l Î sw(M0) sSF++(A)lambda in sigma_{w}(M_{0}) backslash {sigma_{SF_{+}}}+(A) and B has SVEP at points m Î sw(M0) sSF-(B)mu in sigma_{w}(M_{0}) backslash {sigma_{SF_{-}}}(B), or, (ii) both A and A* have SVEP at points l Î sw(M0) sSF+(A)lambda in sigma_{w}(M_{0}) backslash {sigma_{SF_{+}}}(A), or, (iii) A* has SVEP at points l Î sw(M0) sSF+(A)lambda in sigma_{w}(M_{0}) backslash {sigma_{SF_{+}}}(A) and B * has SVEP at points m Î sw(M0) sSF-(B)mu in sigma _{w}(M_{0}) backslash sigma_{SF_{-}}(B), then s(MC) sw(MC) = p0(MC)sigma (M_{C}) backslash sigma_{w}(M_{C}) = pi_{0}(M_{C}). Here the hypothesis that λ ∈ π0(M C ) are poles of the resolvent of A can not be replaced by the hypothesis l Î p0(A)lambda in pi_{0}(A) are poles of the resolvent of A. For an operator T Î B(c)T in B(chi), let p0a(T) = { l: l Î iso sa(T), 0 < dim (T - l)-1(0) < ¥}pi_{0}^{a}(T)= { lambda : lambda in,rm{iso}, sigma_a(T), 0 < , rm{dim},(T - lambda)^{-1}(0)< infty }. We prove that if A* and B* have SVEP, A is polaroid on π a 0(M C) and B is polaroid on π a 0(B), then sa (MC)saw(MC) = pa0(MC)sigma_a (M_C)backslash sigma_{aw}(M_C) = {pi^{a}_{0}}(M_C).
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机译：如果点λ∈isoσ（T）是T的解旋极，则Banach空间算子T∈B（χ）是宝丽来。令s a （T），s w （T），s aw （T），s SF + （T）和s SF -< / sub> （T）sigma_a（T），sigma_w（T），sigma_ {aw}（T），sigma_ {SF _ +}（T），rm {and}，sigma_ {SF _-}（T）分别表示近似点，Weyl，Weyl本质近似，T的上半弗雷德霍姆谱和下半弗雷德霍姆谱。对于A，B和C∈B（χ），令M C 表示运算符矩阵$ left（{{ll} A＆C 0＆B} right）$ left（{begin {array} {ll} A＆C 0＆B end {array}} right）。如果A是p 0 （M C ）上的宝丽来= {lÎiso s（M C ）：0 <暗（M C -l） -1 （0）<¥} pi_ {0}（M_ {C}）= {{lambda in {rm iso}，sigma（M_ {C} ）：0 <{rm dim}（M_ {C}-lambda）^ {-1}（0） 0 满足Weyl定理，并且A和B满足以下任一个假设（i）A在点l s w （M 0 ）s SF + +（ A）sigma_ {w}（M_ {0}）中的反斜杠{sigma_ {SF _ {+}}} +（A）和B在点m s w （M 0 ）s SF - （B）mu in sigma_ {w}（M_ {0}）反斜杠{sigma_ {SF _ {-}}}（（B ），或（ii）A和A *在点l s s w （M 0 ）s SF + （A）sigma_ {w}（M_ {0}）中的反斜杠{sigma_ {SF _ {+}}}（A），或者（iii）A * 具有SVEP在点σs w （M 0 ）s SF + （A）sigma_ {w}中的λ （M_ {0}）反斜杠{sigma_ {SF _ {+}}}（A）和B * 在点m s w （M 0 ）s < sub> SF - （B）mu in sigma _ {w}（M_ {0}）反斜杠sigma_ {SF _ {-}}（B），然后是s（M C ）s w （M C ）= p 0 （M C ）sigma（M_ {C}）反斜杠sigma_ {w}（M_ {C}）= pi_ {0}（M_ {C}）。在这里，λ∈π 0 （M C ）是A的分解体的极点的假设不能由假设lÎp 0 （A）λ是A的旋转角。对于B（chi）中的算子TÎB（c）T，令p 0 a （T）= {l：l iso iso s a （T），0 <昏暗（T-l） -1 （0）<¥ } pi_ {0} ^ {a}（T）= {lambda：lambda in，rm {iso}，sigma_a（T），0 <，rm {dim}，（T-lambda）^ {-1}（0） 0 （M C ）上的宝丽来，B是π上的宝丽来 a 0 （B），然后是s a （M C ）s aw （M C ）= p a 0 （M C ）sigma_a（M_C）反斜杠sigma_ {aw}（ M_C）= {pi ^ {a} _ {0}}（M_C）。
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