<PAGE>   1
                                                    ----------------------------
                                                            OMB APPROVAL
                                                    ----------------------------
                                                    OMB Number:        3235-0145
                                                    Estimated  average
                                                    burden  hours
                                                    per response. . . . . .14.90
                                                    ----------------------------

                                  UNITED STATES
                       SECURITIES AND EXCHANGE COMMISSION
                             WASHINGTON, D.C. 20549


                                  SCHEDULE 13G

         INFORMATION STATEMENT PURSUANT TO RULES 13d-1 (b) AND (c) AND
                 AMENDMENTS THERETO FILED PURSUANT TO 13d-2 (b)

                                (AMENDMENT NO. )*


                                 UAL CORPORATION
                         ------------------------------
                                (Name of Issuer)


                                  COMMON STOCK
                         ------------------------------
                         (Title of Class of Securities)


                                    90254950-0
                         ------------------------------
                                 (CUSIP Number)






        *The remainder of this cover page shall be filled out for a reporting
person's initial filing on this form with respect to the subject class of
securities, and for any subsequent amendment containing information which would
alter the disclosures provided in a prior cover page.

        The information required in the remainder of this cover page shall not
be deemed to be "filed" for the purpose of Section 18 of the Securities Exchange
Act of 1934 ("Act") or otherwise subject to the liabilities of that section of
the Act but shall be subject to all other provisions of the Act (however, see
the Notes).




<PAGE>   2

CUSIP NO. 90254950-0               SCHEDULE 13G               PAGE 2 OF 5 PAGES
          ---------                                              ---  ---
   1      NAME OF REPORTING PERSON
          S.S. or I.R.S. IDENTIFICATION OF ABOVE PERSON

          OPPENHEIMER CAPITAL  (IRS NO. 13-3413767)
- --------- ----------------------------------------------------------------------
   2      CHECK THE APPROPRIATE BOX IF A MEMBER OF A GROUP*              (a) [ ]
                                                                         (b) [x]

- --------- ----------------------------------------------------------------------
   3      SEC USE ONLY


- --------- ----------------------------------------------------------------------
   4      CITIZENSHIP OR PLACE OF ORGANIZATION

          DELAWARE
- -------------------------- ------- ---------------------------------------------
    NUMBER OF SHARES         5     SOLE VOTING POWER
      BENEFICIALLY
        OWNED BY
                                   -0-
                           ------- ---------------------------------------------
          EACH               6     SHARED VOTING POWER
        REPORTING
         PERSON
          WITH                     2,943,650
                           ------- ---------------------------------------------
                             7     SOLE DISPOSITIVE POWER


                                   -0-
                           ------- ---------------------------------------------
                             8     SHARED DISPOSITIVE POWER


                                   2,943,650
- --------- ----------------------------------------------------------------------
   9      AGGREGATE AMOUNT BENEFICIALLY OWNED BY EACH REPORTING PERSON


          2,943,650
- --------- ----------------------------------------------------------------------
   10     CHECK BOX IF THE AGGREGATE AMOUNT IN ROW (9) EXCLUDES CERTAIN SHARES* 
                                                                             [ ]

- --------- ----------------------------------------------------------------------
   11     PERCENT OF CLASS REPRESENTED BY AMOUNT IN ROW (9)


          5.0
- --------- ----------------------------------------------------------------------
   12     TYPE OF REPORTING PERSON*


          IA
- --------- ----------------------------------------------------------------------
                      *SEE INSTRUCTION BEFORE FILLING OUT!





                                       2

<PAGE>   3

ITEM 1 (a) NAME OF ISSUER:
           UAL CORPORATION

       (b) ADDRESS OF ISSUER'S PRINCIPAL EXECUTIVE OFFICES: 
           100 Fillmore Street, Suite 300 
           Denver, CO 80206

ITEM 2 (a) NAME OF PERSON FILING: OPPENHEIMER CAPITAL

       (b) ADDRESS OF PRINCIPAL BUSINESS OFFICE: 
           Oppenheimer Tower, World Financial Center 
           New York, New York 10281

       (c) CITIZENSHIP:
           Not Applicable.

       (d) TITLE OF CLASS OF SECURITIES:
           Common Stock

       (e) CUSIP NUMBER:
           90254950-0

ITEM 3 IF THIS STATEMENT IS FILED PURSUANT TO RULE 13d-1(b), OR 13d-2(b), CHECK
       WHETHER THE PERSON FILING IS A:

       (a) [ ] Broker or Dealer registered under Section 15 of the Act.

       (b) [ ] Bank as defined in Section 3(a)(6) of the Act.

       (c) [ ] Insurance Company as defined in Section 3(a)(19) of the Act.

       (d) [ ] Investment Company registered under Section 8 of the Investment
               Company Act.

       (e) [X] Investment Adviser registered under Section 203 of the Investment
               Advisors Act of 1940.

       (f) [ ] Employee Benefit Plan, Pension Fund which is subject to the
               provisions of the Employee Retirement Income Security Act of 1974
               or Endowment Fund; see Paragraph 240.13d-1(b)(1)(ii)(F).

       (g) [ ] Parent Holding Company, in accordance with 
               Paragraph 13d-1(b)(ii)(G).

       (h) [ ] Group, in accordance with Paragraph 13d-1(b)(1)(ii)(H).



                                       3

<PAGE>   4

ITEM 4 OWNERSHIP.

       (A) Amount beneficially owned: 2,943,650 **

       (B) Percent of Class: 5.0

       (C) Number of shares as to which such person has:

           (i) Sole power to vote or direct the vote: -0-

          (ii) Shared power to vote: 2,943,650 **

         (iii) Sole power to dispose or direct the disposition of: -0-

          (iv) Shared power to dispose or direct the disposition of: 2,943,650**

     **This report is being filed on behalf of Oppenheimer Capital, a Delaware
       general partnership and/or certain investment advisory clients or
       discretionary accounts relating to their collective beneficial ownership
       of shares of common stock of the Issuer. Oppenheimer Capital is a
       registered investment adviser under Section 203 of the Investment
       Advisers Act of 1940. As a result of its role as investment adviser
       Oppenheimer may be deemed to be the beneficial owner of the securities of
       the Issuer. Oppenheimer Capital has the sole power to dispose of the
       shares and to vote the shares under its written guidelines established by
       its Management Board.

       ITEM 5 OWNERSHIP OF FIVE PERCENT OR LESS OF A CLASS.

       If this statement is being filed to report the fact that as of the date
hereof the reporting person has ceased to be the beneficial owner of more than
five percent of the class of securities, check the following [ ].

ITEM 6 OWNERSHIP OF MORE THAN FIVE PERCENT ON BEHALF OF ANOTHER PERSON.

       Our clients have the right to receive or the power to direct the receipt
of dividends or the profits from the sale of such securities. No one client owns
more than five percent of the securities of the Issuer.

ITEM 7 IDENTIFICATION AND CLARIFICATION OF THE SUBSIDIARY WHICH ACQUIRED THE
       SECURITY BEING REPORTED ON BY THE PARENT HOLDING COMPANY.

       Not Applicable.

ITEM 8 IDENTIFICATION AND CLARIFICATION OF MEMBERS OF THE GROUP.

       Not Applicable.

ITEM 9 NOTICE OF DISSOLUTION OF GROUP.

       Not Applicable.



                                       4

<PAGE>   5

ITEM 10 CERTIFICATION.

       By signing below I certify that, to the best of my knowledge and belief,
the securities referred to above were acquired in the ordinary course of
business and were not acquired for the purpose of and do not have the effect of
changing or influencing the control of the issuer of such securities and were
not acquired in connection with or as a participant in any transaction having
such purposes or effect.


                                    SIGNATURE

       After reasonable inquiry and to the best of my knowledge and belief, I
certify that the information set forth in this statement is true, complete and
correct.


                                        Date: February 27, 1998

                                        /s/ THOMAS DUGGAN
                                            -------------------
                                            General Counsel














                                       5