An operator T is said to be paranormal if ｜｜T^2 x ｜｜ 〉｜｜Tx｜｜^2 holds for every unit vector x. Several extensions of paranormal operators are considered until now, for example absolute-k-paranormal and p-paran...An operator T is said to be paranormal if ｜｜T^2 x ｜｜ 〉｜｜Tx｜｜^2 holds for every unit vector x. Several extensions of paranormal operators are considered until now, for example absolute-k-paranormal and p-paranormal introduced in [10], [14], respectively. Yamazaki and Yanagida [38] introduced the class of absolute-（p, r）-paranormal operators as a further generalization of the classes of both absolute-k-paranormal and p-paranormal operators. An operator T ∈ B（H） is called absolute-（p, r）-paranormal operator if ｜｜｜T｜p｜T^＊ ｜^rx｜｜^r 〉 ｜｜｜T^＊｜^rx｜｜p＋r for every unit vector x ∈ H and for positive real numbers p 〉 0 and r 〉 0. The famous result of Browder, that self adjoint operators satisfy Browder＇s theorem, is extended to several classes of operators. In this paper we show that for any absolute-（p, r）- paranormal operator T, T satisfies Browder＇s theorem and a-Browder＇s theorem. It is also shown that if E is the Riesz idempotent for a nonzero isolated point μ of the spectrum of a absolute-（p, r）-paranormal operator T, then E is self-adjoint if and only if the null space of T -μ, N（T - μ） N（T^＊ - ^μ）.展开更多
By combining the classical appropriate functions “1, x, x 2” with the method of multiplier enlargement, this paper establishes a theorem to approximate any unbounded continuous functions with modified positive...By combining the classical appropriate functions “1, x, x 2” with the method of multiplier enlargement, this paper establishes a theorem to approximate any unbounded continuous functions with modified positive linear operators. As an example, Hermite Fejér interpolation polynomial operators are analysed and studied, and a general conclusion is obtained.展开更多
A theory of reverse triple I method with sustention degree is presented by using the implication operator R0 in every step of the fuzzy reasoning. Its computation formulas of supremum for fuzzy modus ponens and infimu...A theory of reverse triple I method with sustention degree is presented by using the implication operator R0 in every step of the fuzzy reasoning. Its computation formulas of supremum for fuzzy modus ponens and infimum for fuzzy modus tollens are given respectively. Moreover, through the generalization of this problem, the corresponding formulas of α-reverse triple I method with sustention degree are also obtained. In addition, the theory of reverse triple I method with restriction degree is proposed as well by using the operator R0, and the computation formulas of infimum for fuzzy modus ponens and supremum for fuzzy modus tollens are shown.展开更多
基金supported by Taibah University Research Center Project(1433/803)
文摘An operator T is said to be paranormal if ｜｜T^2 x ｜｜ 〉｜｜Tx｜｜^2 holds for every unit vector x. Several extensions of paranormal operators are considered until now, for example absolute-k-paranormal and p-paranormal introduced in [10], [14], respectively. Yamazaki and Yanagida [38] introduced the class of absolute-（p, r）-paranormal operators as a further generalization of the classes of both absolute-k-paranormal and p-paranormal operators. An operator T ∈ B（H） is called absolute-（p, r）-paranormal operator if ｜｜｜T｜p｜T^＊ ｜^rx｜｜^r 〉 ｜｜｜T^＊｜^rx｜｜p＋r for every unit vector x ∈ H and for positive real numbers p 〉 0 and r 〉 0. The famous result of Browder, that self adjoint operators satisfy Browder＇s theorem, is extended to several classes of operators. In this paper we show that for any absolute-（p, r）- paranormal operator T, T satisfies Browder＇s theorem and a-Browder＇s theorem. It is also shown that if E is the Riesz idempotent for a nonzero isolated point μ of the spectrum of a absolute-（p, r）-paranormal operator T, then E is self-adjoint if and only if the null space of T -μ, N（T - μ） N（T^＊ - ^μ）.
文摘By combining the classical appropriate functions “1, x, x 2” with the method of multiplier enlargement, this paper establishes a theorem to approximate any unbounded continuous functions with modified positive linear operators. As an example, Hermite Fejér interpolation polynomial operators are analysed and studied, and a general conclusion is obtained.
基金This work was supported by the National Natural Science Foundation of China (Grant Nos.60074015, 60004010) and Basal Research Foundations of Tsinghua University (Grant No. JC2001029) and 985 Basic Research Foundation of the School of Information Sc
文摘A theory of reverse triple I method with sustention degree is presented by using the implication operator R0 in every step of the fuzzy reasoning. Its computation formulas of supremum for fuzzy modus ponens and infimum for fuzzy modus tollens are given respectively. Moreover, through the generalization of this problem, the corresponding formulas of α-reverse triple I method with sustention degree are also obtained. In addition, the theory of reverse triple I method with restriction degree is proposed as well by using the operator R0, and the computation formulas of infimum for fuzzy modus ponens and supremum for fuzzy modus tollens are shown.
