## Linear Operators: General theory |

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Page 45

With this notation the number expressed by the sum 11 = 1 in , . . . , in air , 19 • . . .

dinen in = 1 is called the determinant of the

then it can be shown that the determinants of the

With this notation the number expressed by the sum 11 = 1 in , . . . , in air , 19 • . . .

dinen in = 1 is called the determinant of the

**matrix**( aij ) . If T is a linear operator ,then it can be shown that the determinants of the

**matrices**of T in terms of any ...Page 75

Suppose that a

means of the formula T [ S1 , S2 , . . . ] = [ 1 , tz , . . . ] = [ X ajSj , & Q2jSj , . . . ) . j = 1

j = 1 If T preserves limits of sequences ( i . e . if limiza ti = lim s ; for every [ si ] e c )

...

Suppose that a

**matrix**( aij ) defines a linear transformation T of c into itself bymeans of the formula T [ S1 , S2 , . . . ] = [ 1 , tz , . . . ] = [ X ajSj , & Q2jSj , . . . ) . j = 1

j = 1 If T preserves limits of sequences ( i . e . if limiza ti = lim s ; for every [ si ] e c )

...

Page 607

Polynomials of a

by 1867 Laguerre [ 1 ] had considered infinite power series in a

constructing the exponential function of a

arbitrary ...

Polynomials of a

**matrix**were used almost from the beginning of the theory , andby 1867 Laguerre [ 1 ] had considered infinite power series in a

**matrix**inconstructing the exponential function of a

**matrix**. Sylvester [ 1 , 2 ] constructedarbitrary ...

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### Contents

Special Spaces | 237 |

Convex Sets and Weak Topologies | 409 |

General Spectral Theory | 555 |

Copyright | |

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