Ck Il xii k Il y!1 k

- 19 -

Il ^B(x,y) il ^k

_Ck Il ^{xii k} Il ^{y!1 k}

o o

(x,yeE).

However, we ha ve the following somewhat surprlslng result from the structure theory:

THEOREt-i 5.

M.pa/l.i0teJ.y bO(ll1de.d tlUJ"lc:ua,"

jo.L.l.tJ'.y bOtU1ded. ^Il.'l

caoJtcUna:te ~u.b~pacej,

.th.u., .j.ta:tcmen.t .u., j)auc.

00

C

IT)

o 6w

In the light of this result, I feel quite uncertain as to the exact reason

for the difference between Theorem 2 and Theorem 2'. Is the latter in some sense stronger or are the hypotheses actual1y equivalent? Perhaps future research will explain the matter.

R E F E R E N C E 5

[lJ Ed oUBINSKY,

MJtLlc.:twre 06

FIt(c.lte:t

72o,Springer-Verlag (1979) .

Ed DUBINSKY, NOn-u.,"Call.

.lpac.el, to appear .

• •

G.KOTHE,

Ul1eall. Réiwne, Springer-Verlag (1960).

14IS.~OJASIEWICZ,

Jr. and E.ZEHNoER, An inverse function theorem in Fréchet spaces, J.FW1C.:t. AnaL. 33 (1979) 165-174.

[5J B.S.MITIAGIN, Approximative dimension and bases ln nuclear spaces (Russian) Ulp.

16 (4) (1961) 73-132.

[6] J.MOSER, A new technique for the construction of solutions of nonlinear differ enti al equations,

Na:t.

(1961) 1824-1831.

[7] J.NASH, The embedding problem for Riemannian manifolds, Ann. 06

63 (1956) 20-63.

[8J J.T.SCHWARTS,

6ul.1c.:UonaL al.'laLlj.lù (1963-1964), Courant Institute, NYU (1965).

r9J o.VoGT, Carakterisierung der Unterraume von s,

2.155 (1977) 109-117.

[lOJ o.VOGT, Subspaces and quotient spaces of (s),

SU!l.vey<.

al.'ld _Itec.e~

lteluU;", Proc.Conf.Paderborn (1976),North-Holland (1977) 167-187.

['11] o.VOGT, Charakterisierung der Unterraume eines nuklearen stabilen Potenzreihen raumes von endlichen Typ,

Ma:th.,to appear.

o.VORT and M.J.WAGNER, Charakterisierung der Unteraume und Quotientenraume der nuklea.'e s,1;attH,eQ potenzreihen Raume von unendlichen Typ.

~~~--., ~~

to appear ..:;} /c,;." '\.~,

DI'

~ ^{( ;} "~·[I", ^{\ .}

". ' l ' "''')~'I

..., -·-"e "':'_

:-;;. , ·7:,)1;~Ì1 :;::j D1PART1MENTO DI i\lATm.ll\T!CA

~.~~~~

inven!ar;o.Ol~J.j.t ^...

...